The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
Lourenco Beirão da Veiga, Carlo Lovadina, Giuseppe Vacca
ESAIM: M2AN, 51 2 (2017) 509-535
Published online: 2017-02-20
This article has been cited by the following article(s):
Ill-conditioning in the virtual element method: Stabilizations and bases
Lorenzo Mascotto
Numerical Methods for Partial Differential Equations 34 (4) 1258 (2018)
DOI: 10.1002/num.22257
See this article
Exponential convergence of the hp virtual element method in presence of corner singularities
L. Beirão da Veiga, A. Chernov, L. Mascotto and A. Russo
Numerische Mathematik 138 (3) 581 (2018)
DOI: 10.1007/s00211-017-0921-7
See this article
A pressure-robust virtual element method for the Navier-Stokes problem on polygonal mesh
Ying Wang, Gang Wang and Yue Shen
Computers & Mathematics with Applications 131 124 (2023)
DOI: 10.1016/j.camwa.2022.12.013
See this article
Conforming and nonconforming conservative virtual element methods for nonlinear Schrödinger equation: A unified framework
Meng Li, Jikun Zhao, Nan Wang and Shaochun Chen
Computer Methods in Applied Mechanics and Engineering 380 113793 (2021)
DOI: 10.1016/j.cma.2021.113793
See this article
Enrichment of the nonconforming virtual element method with singular functions
E. Artioli and L. Mascotto
Computer Methods in Applied Mechanics and Engineering 385 114024 (2021)
DOI: 10.1016/j.cma.2021.114024
See this article
A priori error analysis for a mixed VEM discretization of the spectral problem for the Laplacian operator
Felipe Lepe and Gonzalo Rivera
Calcolo 58 (2) (2021)
DOI: 10.1007/s10092-021-00412-x
See this article
Piecewise Divergence-Free Nonconforming Virtual Elements for Stokes Problem in Any Dimensions
Huayi Wei, Xuehai Huang and Ao Li
SIAM Journal on Numerical Analysis 59 (3) 1835 (2021)
DOI: 10.1137/20M1350479
See this article
Convergence analysis of virtual element methods for semilinear parabolic problems on polygonal meshes
Dibyendu Adak, E. Natarajan and Sarvesh Kumar
Numerical Methods for Partial Differential Equations 35 (1) 222 (2019)
DOI: 10.1002/num.22298
See this article
A dual hybrid virtual element method for plane elasticity problems
Edoardo Artioli, Stefano de Miranda, Carlo Lovadina and Luca Patruno
ESAIM: Mathematical Modelling and Numerical Analysis 54 (5) 1725 (2020)
DOI: 10.1051/m2an/2020011
See this article
A virtual element method for the acoustic vibration problem
Lourenço Beirão da Veiga, David Mora, Gonzalo Rivera and Rodolfo Rodríguez
Numerische Mathematik 136 (3) 725 (2017)
DOI: 10.1007/s00211-016-0855-5
See this article
Stability and Interpolation Properties for Stokes-Like Virtual Element Spaces
Jian Meng, Lourenço Beirão da Veiga and Lorenzo Mascotto
Journal of Scientific Computing 94 (3) (2023)
DOI: 10.1007/s10915-023-02112-w
See this article
A low-order locking-free virtual element for linear elasticity problems
Xialan Tang, Zhibin Liu, Baiju Zhang and Minfu Feng
Computers & Mathematics with Applications 80 (5) 1260 (2020)
DOI: 10.1016/j.camwa.2020.04.032
See this article
Virtual element for the buckling problem of Kirchhoff–Love plates
David Mora and Iván Velásquez
Computer Methods in Applied Mechanics and Engineering 360 112687 (2020)
DOI: 10.1016/j.cma.2019.112687
See this article
Mimetic finite difference methods for Hamiltonian wave equations in 2D
L. Beirão da Veiga, L. Lopez and G. Vacca
Computers & Mathematics with Applications 74 (5) 1123 (2017)
DOI: 10.1016/j.camwa.2017.05.022
See this article
An adaptive virtual element method for incompressible flow
Ying Wang, Gang Wang and Feng Wang
Computers & Mathematics with Applications 101 63 (2021)
DOI: 10.1016/j.camwa.2021.09.012
See this article
Generalized weak Galerkin methods for Stokes equations
Wenya Qi, Padmanabhan Seshaiyer and Junping Wang
Computers & Mathematics with Applications 134 181 (2023)
DOI: 10.1016/j.camwa.2023.01.014
See this article
Virtual element method for semilinear elliptic problems on polygonal meshes
D. Adak, S. Natarajan and E. Natarajan
Applied Numerical Mathematics 145 175 (2019)
DOI: 10.1016/j.apnum.2019.05.021
See this article
A Hybrid High-Order Method for the Steady Incompressible Navier–Stokes Problem
Daniele A. Di Pietro and Stella Krell
Journal of Scientific Computing 74 (3) 1677 (2018)
DOI: 10.1007/s10915-017-0512-x
See this article
A stress/displacement Virtual Element method for plane elasticity problems
E. Artioli, S. de Miranda, C. Lovadina and L. Patruno
Computer Methods in Applied Mechanics and Engineering 325 155 (2017)
DOI: 10.1016/j.cma.2017.06.036
See this article
Stability analysis for the virtual element method
Lourenço Beirão da Veiga, Carlo Lovadina and Alessandro Russo
Mathematical Models and Methods in Applied Sciences 27 (13) 2557 (2017)
DOI: 10.1142/S021820251750052X
See this article
High-order Virtual Element Method on polyhedral meshes
L. Beirão da Veiga, F. Dassi and A. Russo
Computers & Mathematics with Applications 74 (5) 1110 (2017)
DOI: 10.1016/j.camwa.2017.03.021
See this article
Virtual element method for semilinear hyperbolic problems on polygonal meshes
Dibyendu Adak, E. Natarajan and Sarvesh Kumar
International Journal of Computer Mathematics 96 (5) 971 (2019)
DOI: 10.1080/00207160.2018.1475651
See this article
Virtual Elements for the Navier--Stokes Problem on Polygonal Meshes
L. Beira͂o da Veiga, C. Lovadina and G. Vacca
SIAM Journal on Numerical Analysis 56 (3) 1210 (2018)
DOI: 10.1137/17M1132811
See this article
Polynomial preserving virtual elements with curved edges
L. Beirão da Veiga, F. Brezzi, L. D. Marini and A. Russo
Mathematical Models and Methods in Applied Sciences 30 (08) 1555 (2020)
DOI: 10.1142/S0218202520500311
See this article
A mixed virtual element method for a nonlinear Brinkman model of porous media flow
Gabriel N. Gatica, Mauricio Munar and Filánder A. Sequeira
Calcolo 55 (2) (2018)
DOI: 10.1007/s10092-018-0262-7
See this article
The nonconforming virtual element method for the Darcy–Stokes problem
Jikun Zhao, Bei Zhang, Shipeng Mao and Shaochun Chen
Computer Methods in Applied Mechanics and Engineering 370 113251 (2020)
DOI: 10.1016/j.cma.2020.113251
See this article
An H1-conforming virtual element for Darcy and Brinkman equations
Giuseppe Vacca
Mathematical Models and Methods in Applied Sciences 28 (01) 159 (2018)
DOI: 10.1142/S0218202518500057
See this article
On the Coupling of VEM and BEM in Two and Three Dimensions
Gabriel N. Gatica and Salim Meddahi
SIAM Journal on Numerical Analysis 57 (6) 2493 (2019)
DOI: 10.1137/18M1202487
See this article
The fully nonconforming virtual element method for biharmonic problems
P. F. Antonietti, G. Manzini and M. Verani
Mathematical Models and Methods in Applied Sciences 28 (02) 387 (2018)
DOI: 10.1142/S0218202518500100
See this article
A nonconforming virtual element method for the Stokes problem on general meshes
Xin Liu, Jian Li and Zhangxin Chen
Computer Methods in Applied Mechanics and Engineering 320 694 (2017)
DOI: 10.1016/j.cma.2017.03.027
See this article
Virtual element method for two-dimensional linear elasticity problem in mixed weakly symmetric formulation
Baiju Zhang and Minfu Feng
Applied Mathematics and Computation 328 1 (2018)
DOI: 10.1016/j.amc.2018.01.023
See this article
The Stokes Complex for Virtual Elements with Application to Navier–Stokes Flows
L. Beirão da Veiga, D. Mora and G. Vacca
Journal of Scientific Computing 81 (2) 990 (2019)
DOI: 10.1007/s10915-019-01049-3
See this article
A Posteriori Error Estimates for the Virtual Element Method for the Stokes Problem
Gang Wang, Ying Wang and Yinnian He
Journal of Scientific Computing 84 (2) (2020)
DOI: 10.1007/s10915-020-01281-2
See this article
Virtual element method for second-order elliptic eigenvalue problems
Francesca Gardini and Giuseppe Vacca
IMA Journal of Numerical Analysis 38 (4) 2026 (2018)
DOI: 10.1093/imanum/drx063
See this article
Stabilized virtual element methods for the unsteady incompressible Navier–Stokes equations
Diego Irisarri and Guillermo Hauke
Calcolo 56 (4) (2019)
DOI: 10.1007/s10092-019-0332-5
See this article
A nonconforming Trefftz virtual element method for the Helmholtz problem
Lorenzo Mascotto, Ilaria Perugia and Alexander Pichler
Mathematical Models and Methods in Applied Sciences 29 (09) 1619 (2019)
DOI: 10.1142/S0218202519500301
See this article
A mixed virtual element method for the vibration problem of clamped Kirchhoff plate
Jian Meng and Liquan Mei
Advances in Computational Mathematics 46 (5) (2020)
DOI: 10.1007/s10444-020-09810-1
See this article
Virtual element method for elliptic bulk‐surface PDEs in three space dimensions
Massimo Frittelli, Anotida Madzvamuse and Ivonne Sgura
Numerical Methods for Partial Differential Equations (2023)
DOI: 10.1002/num.23040
See this article
Virtual element methods for the obstacle problem
Fei Wang and Huayi Wei
IMA Journal of Numerical Analysis (2018)
DOI: 10.1093/imanum/dry055
See this article
Efficient multi-material continuum topology optimization considering hyperelasticity: Achieving local feature control through regional constraints
Xiaojia Shelly Zhang and Heng Chi
Mechanics Research Communications 105 103494 (2020)
DOI: 10.1016/j.mechrescom.2020.103494
See this article
BDDC and FETI-DP for the virtual element method
Silvia Bertoluzza, Micol Pennacchio and Daniele Prada
Calcolo 54 (4) 1565 (2017)
DOI: 10.1007/s10092-017-0242-3
See this article
A mixed virtual element method for the Navier–Stokes equations
Gabriel N. Gatica, Mauricio Munar and Filánder A. Sequeira
Mathematical Models and Methods in Applied Sciences 28 (14) 2719 (2018)
DOI: 10.1142/S0218202518500598
See this article
Analysis of divergence free conforming virtual elements for the Brinkman problem
Xuehai Huang and Feng Wang
Mathematical Models and Methods in Applied Sciences 33 (06) 1245 (2023)
DOI: 10.1142/S021820252350029X
See this article
A Hybrid High-Order method for the incompressible Navier–Stokes equations based on Temam's device
Lorenzo Botti, Daniele A. Di Pietro and Jérôme Droniou
Journal of Computational Physics 376 786 (2019)
DOI: 10.1016/j.jcp.2018.10.014
See this article
Non-conforming Harmonic Virtual Element Method: $$h$$h- and $$p$$p-Versions
Lorenzo Mascotto, Ilaria Perugia and Alexander Pichler
Journal of Scientific Computing 77 (3) 1874 (2018)
DOI: 10.1007/s10915-018-0797-4
See this article
Equilibrium analysis of an immersed rigid leaflet by the virtual element method
L. Beirão da Veiga, C. Canuto, R. H. Nochetto and G. Vacca
Mathematical Models and Methods in Applied Sciences 31 (07) 1323 (2021)
DOI: 10.1142/S0218202521500275
See this article
A Mixed Virtual Element Method for Quasi-Newtonian Stokes Flows
Ernesto Cáceres, Gabriel N. Gatica and Filánder A. Sequeira
SIAM Journal on Numerical Analysis 56 (1) 317 (2018)
DOI: 10.1137/17M1121160
See this article
A Family of Three-Dimensional Virtual Elements with Applications to Magnetostatics
L. Beira͂o da Veiga, F. Brezzi, F. Dassi, L. D. Marini and A. Russo
SIAM Journal on Numerical Analysis 56 (5) 2940 (2018)
DOI: 10.1137/18M1169886
See this article
A virtual element method for stochastic Stokes equations
Wei Liu and Huoyuan Duan
Computers & Mathematics with Applications (2019)
DOI: 10.1016/j.camwa.2019.10.005
See this article
The nonconforming virtual element method for elasticity problems
Bei Zhang, Jikun Zhao, Yongqin Yang and Shaochun Chen
Journal of Computational Physics 378 394 (2019)
DOI: 10.1016/j.jcp.2018.11.004
See this article
A virtual element method for the transmission eigenvalue problem
David Mora and Iván Velásquez
Mathematical Models and Methods in Applied Sciences 28 (14) 2803 (2018)
DOI: 10.1142/S0218202518500616
See this article
A priori and a posteriori error estimates for a virtual element spectral analysis for the elasticity equations
David Mora and Gonzalo Rivera
IMA Journal of Numerical Analysis (2018)
DOI: 10.1093/imanum/dry063
See this article
Serendipity Virtual Elements for General Elliptic Equations in Three Dimensions
Lourenço Beirão Da Veiga, Franco Brezzi, Franco Dassi, Luisa Donatelia Marini and Alessandro Russo
Chinese Annals of Mathematics, Series B 39 (2) 315 (2018)
DOI: 10.1007/s11401-018-1066-4
See this article
A virtual element method for a nonlocal FitzHugh–Nagumo model of cardiac electrophysiology
Mauricio Sepúlveda, David Mora, Mostafa Bendahmane and Verónica Anaya
IMA Journal of Numerical Analysis 40 (2) 1544 (2020)
DOI: 10.1093/imanum/drz001
See this article
The nonconforming virtual element method for the Navier-Stokes equations
Xin Liu and Zhangxin Chen
Advances in Computational Mathematics 45 (1) 51 (2019)
DOI: 10.1007/s10444-018-9602-z
See this article
A Divergence Free Weak Virtual Element Method for the Stokes Problem on Polytopal Meshes
Long Chen and Feng Wang
Journal of Scientific Computing 78 (2) 864 (2019)
DOI: 10.1007/s10915-018-0796-5
See this article
Basic convergence theory for the network element method
Julien Coatléven
ESAIM: Mathematical Modelling and Numerical Analysis 55 (5) 2503 (2021)
DOI: 10.1051/m2an/2021062
See this article
An Advection-Robust Hybrid High-Order Method for the Oseen Problem
Joubine Aghili and Daniele A. Di Pietro
Journal of Scientific Computing 77 (3) 1310 (2018)
DOI: 10.1007/s10915-018-0681-2
See this article
Virtual element method for nonlinear convection–diffusion–reaction equation on polygonal meshes
M. Arrutselvi and E. Natarajan
International Journal of Computer Mathematics 98 (9) 1852 (2021)
DOI: 10.1080/00207160.2020.1849637
See this article
Bricks for the mixed high-order virtual element method: Projectors and differential operators
F. Dassi and G. Vacca
Applied Numerical Mathematics 155 140 (2020)
DOI: 10.1016/j.apnum.2019.03.014
See this article
A virtual element method for the coupled Stokes–Darcy problem with the Beaver–Joseph–Saffman interface condition
Xin Liu, Rui Li and Zhangxin Chen
Calcolo 56 (4) (2019)
DOI: 10.1007/s10092-019-0345-0
See this article
A fully discrete virtual element scheme for the Cahn–Hilliard equation in mixed form
Xin Liu, Zhengkang He and Zhangxin Chen
Computer Physics Communications 246 106870 (2020)
DOI: 10.1016/j.cpc.2019.106870
See this article
A divergence-free reconstruction of the nonconforming virtual element method for the Stokes problem
Xin Liu, Rui Li and Yufeng Nie
Computer Methods in Applied Mechanics and Engineering 372 113351 (2020)
DOI: 10.1016/j.cma.2020.113351
See this article
Parallel block preconditioners for three-dimensional virtual element discretizations of saddle-point problems
F. Dassi and S. Scacchi
Computer Methods in Applied Mechanics and Engineering 372 113424 (2020)
DOI: 10.1016/j.cma.2020.113424
See this article
Virtual Element approximation of 2D magnetostatic problems
L. Beirão da Veiga, F. Brezzi, F. Dassi, L.D. Marini and A. Russo
Computer Methods in Applied Mechanics and Engineering 327 173 (2017)
DOI: 10.1016/j.cma.2017.08.013
See this article
The Divergence-Free Nonconforming Virtual Element for the Stokes Problem
Jikun Zhao, Bei Zhang, Shipeng Mao and Shaochun Chen
SIAM Journal on Numerical Analysis 57 (6) 2730 (2019)
DOI: 10.1137/18M1200762
See this article
The Nonconforming Virtual Element Method for a Stationary Stokes Hemivariational Inequality with Slip Boundary Condition
Min Ling, Fei Wang and Weimin Han
Journal of Scientific Computing 85 (3) (2020)
DOI: 10.1007/s10915-020-01333-7
See this article
On the application of polygonal finite element method for Stokes flow – A comparison between equal order and different order approximation
Sundararajan Natarajan
Computer Aided Geometric Design 77 101813 (2020)
DOI: 10.1016/j.cagd.2019.101813
See this article
A family of virtual element methods for plane elasticity problems based on the Hellinger–Reissner principle
E. Artioli, S. de Miranda, C. Lovadina and L. Patruno
Computer Methods in Applied Mechanics and Engineering 340 978 (2018)
DOI: 10.1016/j.cma.2018.06.020
See this article
The curl–curl conforming virtual element method for the quad-curl problem
Jikun Zhao and Bei Zhang
Mathematical Models and Methods in Applied Sciences 31 (08) 1659 (2021)
DOI: 10.1142/S0218202521500354
See this article
The Stokes complex for Virtual Elements in three dimensions
L. Beirão da Veiga, F. Dassi and G. Vacca
Mathematical Models and Methods in Applied Sciences 30 (03) 477 (2020)
DOI: 10.1142/S0218202520500128
See this article
A local projection stabilization virtual element method for convection-diffusion-reaction equation
Yang Li and Minfu Feng
Applied Mathematics and Computation 411 126536 (2021)
DOI: 10.1016/j.amc.2021.126536
See this article
Virtual element methods for nonlocal parabolic problems on general type of meshes
D. Adak and S. Natarajan
Advances in Computational Mathematics 46 (5) (2020)
DOI: 10.1007/s10444-020-09811-0
See this article
The nonconforming Virtual Element Method for eigenvalue problems
Francesca Gardini, Gianmarco Manzini and Giuseppe Vacca
ESAIM: Mathematical Modelling and Numerical Analysis 53 (3) 749 (2019)
DOI: 10.1051/m2an/2018074
See this article
The Virtual Element Method with curved edges
L. Beirão da Veiga, A. Russo and G. Vacca
ESAIM: Mathematical Modelling and Numerical Analysis 53 (2) 375 (2019)
DOI: 10.1051/m2an/2018052
See this article
A Hybrid High-Order method for the incompressible Navier–Stokes problem robust for large irrotational body forces
Daniel Castanon Quiroz and Daniele A. Di Pietro
Computers & Mathematics with Applications 79 (9) 2655 (2020)
DOI: 10.1016/j.camwa.2019.12.005
See this article
On the $${ H}^{1}$$ Conforming Virtual Element Method for Time Dependent Stokes Equation
Dibyendu Adak and Sundararajan Natarajan
Mathematics in Computer Science 15 (1) 135 (2021)
DOI: 10.1007/s11786-020-00473-1
See this article
Virtual element method for a nonlocal elliptic problem of Kirchhoff type on polygonal meshes
D. Adak and S. Natarajan
Computers & Mathematics with Applications 79 (10) 2856 (2020)
DOI: 10.1016/j.camwa.2019.12.018
See this article
Relationship between the vertex-centered linearity-preserving scheme and the lowest-order virtual element method for diffusion problems on star-shaped polygons
Qiannan Dong, Jiming Wu and Shuai Su
Computers & Mathematics with Applications 79 (11) 3117 (2020)
DOI: 10.1016/j.camwa.2020.01.009
See this article
A virtual element method for the Laplacian eigenvalue problem in mixed form
Jian Meng, Yongchao Zhang and Liquan Mei
Applied Numerical Mathematics 156 1 (2020)
DOI: 10.1016/j.apnum.2020.03.026
See this article
Conforming and nonconforming virtual element methods for a Kirchhoff plate contact problem
Fei Wang and Jikun Zhao
IMA Journal of Numerical Analysis 41 (2) 1496 (2021)
DOI: 10.1093/imanum/draa005
See this article
The Hybrid High-Order Method for Polytopal Meshes
Daniele Antonio Di Pietro and Jérôme Droniou
MS&A, The Hybrid High-Order Method for Polytopal Meshes 19 381 (2020)
DOI: 10.1007/978-3-030-37203-3_8
See this article
FETI-DP for the Three Dimensional Virtual Element Method
Silvia Bertoluzza, Micol Pennacchio and Daniele Prada
SIAM Journal on Numerical Analysis 58 (3) 1556 (2020)
DOI: 10.1137/18M1233303
See this article
A posteriori error estimation and adaptivity in hp virtual elements
L. Beirão da Veiga, G. Manzini and L. Mascotto
Numerische Mathematik 143 (1) 139 (2019)
DOI: 10.1007/s00211-019-01054-6
See this article
A posteriori error analysis of a mixed virtual element method for a nonlinear Brinkman model of porous media flow
Mauricio Munar and Filánder A. Sequeira
Computers & Mathematics with Applications 80 (5) 1240 (2020)
DOI: 10.1016/j.camwa.2020.06.005
See this article
Bulk-surface virtual element method for systems of PDEs in two-space dimensions
Massimo Frittelli, Anotida Madzvamuse and Ivonne Sgura
Numerische Mathematik 147 (2) 305 (2021)
DOI: 10.1007/s00211-020-01167-3
See this article
Virtual element methods for the three-field formulation of time-dependent linear poroelasticity
Raimund Bürger, Sarvesh Kumar, David Mora, Ricardo Ruiz-Baier and Nitesh Verma
Advances in Computational Mathematics 47 (1) (2021)
DOI: 10.1007/s10444-020-09826-7
See this article
Robust nonconforming virtual element methods for general fourth-order problems with varying coefficients
Andreas Dedner and Alice Hodson
IMA Journal of Numerical Analysis 42 (2) 1364 (2022)
DOI: 10.1093/imanum/drab003
See this article
A virtual element approximation for the pseudostress formulation of the Stokes eigenvalue problem
Felipe Lepe and Gonzalo Rivera
Computer Methods in Applied Mechanics and Engineering 379 113753 (2021)
DOI: 10.1016/j.cma.2021.113753
See this article
A Hybrid High-Order discretisation of the Brinkman problem robust in the Darcy and Stokes limits
Lorenzo Botti, Daniele A. Di Pietro and Jérôme Droniou
Computer Methods in Applied Mechanics and Engineering 341 278 (2018)
DOI: 10.1016/j.cma.2018.07.004
See this article
On nonconvex meshes for elastodynamics using virtual element methods with explicit time integration
Kyoungsoo Park, Heng Chi and Glaucio H. Paulino
Computer Methods in Applied Mechanics and Engineering 356 669 (2019)
DOI: 10.1016/j.cma.2019.06.031
See this article
A hybrid high-order method for creeping flows of non-Newtonian fluids
Michele Botti, Daniel Castanon Quiroz, Daniele A. Di Pietro and André Harnist
ESAIM: Mathematical Modelling and Numerical Analysis 55 (5) 2045 (2021)
DOI: 10.1051/m2an/2021051
See this article
Divergence-free Scott--Vogelius Elements on Curved Domains
Michael Neilan and Baris Otus
SIAM Journal on Numerical Analysis 59 (2) 1090 (2021)
DOI: 10.1137/20M1360098
See this article
p- and hp- virtual elements for the Stokes problem
A. Chernov, C. Marcati and L. Mascotto
Advances in Computational Mathematics 47 (2) (2021)
DOI: 10.1007/s10444-020-09831-w
See this article
A C0 virtual element method for the biharmonic eigenvalue problem
Jian Meng and Liquan Mei
International Journal of Computer Mathematics 98 (9) 1821 (2021)
DOI: 10.1080/00207160.2020.1849635
See this article
A projection-based stabilized virtual element method for the unsteady incompressible Brinkman equations
Xi Zhang and Minfu Feng
Applied Mathematics and Computation 408 126325 (2021)
DOI: 10.1016/j.amc.2021.126325
See this article
A modified nonconforming virtual element with BDM-like reconstruction for the Navier-Stokes equations
Xin Liu and Yufeng Nie
Applied Numerical Mathematics 167 375 (2021)
DOI: 10.1016/j.apnum.2021.05.014
See this article
A pressure-robust virtual element method for the Stokes problem
Gang Wang, Lin Mu, Ying Wang and Yinnian He
Computer Methods in Applied Mechanics and Engineering 382 113879 (2021)
DOI: 10.1016/j.cma.2021.113879
See this article
Principles of a network element method
Julien Coatléven
Journal of Computational Physics 433 110197 (2021)
DOI: 10.1016/j.jcp.2021.110197
See this article
A C1 virtual element method for the stationary quasi-geostrophic equations of the ocean
David Mora and Alberth Silgado
Computers & Mathematics with Applications 116 212 (2022)
DOI: 10.1016/j.camwa.2021.05.022
See this article
Ella P. Shurina, Daria V. Dobroliubova and Ekaterina I. Shtanko
283 (2018)
DOI: 10.1109/APEIE.2018.8545270
See this article
Variable-time-step BDF2 nonconforming VEM for coupled Ginzburg-Landau equations
Meng Li, Lingli Wang and Nan Wang
Applied Numerical Mathematics 186 378 (2023)
DOI: 10.1016/j.apnum.2023.01.022
See this article
A New Projection-Based Stabilized Virtual Element Method for the Stokes Problem
Jun Guo and Minfu Feng
Journal of Scientific Computing 85 (1) (2020)
DOI: 10.1007/s10915-020-01301-1
See this article
Polyhedral Methods in Geosciences
Dibyendu Adak, Gianmarco Manzini and Sundararajan Natarajan
SEMA SIMAI Springer Series, Polyhedral Methods in Geosciences 27 259 (2021)
DOI: 10.1007/978-3-030-69363-3_7
See this article
Lowest order virtual element approximations for transient Stokes problem on polygonal meshes
N. Verma and S. Kumar
Calcolo 58 (4) (2021)
DOI: 10.1007/s10092-021-00440-7
See this article
A virtual element discretization for the time dependent Navier–Stokes equations in stream-function formulation
Dibyendu Adak, David Mora, Sundararajan Natarajan and Alberth Silgado
ESAIM: Mathematical Modelling and Numerical Analysis 55 (5) 2535 (2021)
DOI: 10.1051/m2an/2021058
See this article
A Divergence-Free Stabilized Finite Element Method for the Evolutionary Navier--Stokes Equations
Alejandro Allendes, Gabriel R. Barrenechea and Julia Novo
SIAM Journal on Scientific Computing 43 (6) A3809 (2021)
DOI: 10.1137/21M1394709
See this article
A divergence-free weak virtual element method for the Navier-Stokes equation on polygonal meshes
Gang Wang, Feng Wang and Yinnian He
Advances in Computational Mathematics 47 (6) (2021)
DOI: 10.1007/s10444-021-09909-z
See this article
A discontinuous Galerkin method for mathematical simulating of gas-liquid mixture flows
E P Shurina, N B Itkina and S I Markov
Journal of Physics: Conference Series 1615 (1) 012009 (2020)
DOI: 10.1088/1742-6596/1615/1/012009
See this article
Two robust virtual element methods for the Brinkman equations
Gang Wang, Ying Wang and Yinnian He
Calcolo 58 (4) (2021)
DOI: 10.1007/s10092-021-00442-5
See this article
Virtual element stabilization of convection-diffusion equation with shock capturing
M. Arrutselvi and E. Natarajan
Journal of Physics: Conference Series 1850 (1) 012001 (2021)
DOI: 10.1088/1742-6596/1850/1/012001
See this article
A C1-virtual element method of high order for the Brinkman equations in stream function formulation with pressure recovery
David Mora, Carlos Reales and Alberth Silgado
IMA Journal of Numerical Analysis 42 (4) 3632 (2022)
DOI: 10.1093/imanum/drab078
See this article
A virtual element generalization on polygonal meshes of the Scott-Vogelius finite element method for the 2-D Stokes problem
Gianmarco Manzini and Annamaria Mazzia
Journal of Computational Dynamics 9 (2) 207 (2022)
DOI: 10.3934/jcd.2021020
See this article
Lowest-order virtual element methods for linear elasticity problems
Do Y. Kwak and Hyeokjoo Park
Computer Methods in Applied Mechanics and Engineering 390 114448 (2022)
DOI: 10.1016/j.cma.2021.114448
See this article
A virtual element method for the two-phase flow of immiscible fluids in porous media
Stefano Berrone and Martina Busetto
Computational Geosciences 26 (1) 195 (2022)
DOI: 10.1007/s10596-021-10116-4
See this article
Divergence-preserving reconstructions on polygons and a really pressure-robust virtual element method for the Stokes problem
Derk Frerichs and Christian Merdon
IMA Journal of Numerical Analysis 42 (1) 597 (2022)
DOI: 10.1093/imanum/draa073
See this article
Stability Analysis of Polytopic Discontinuous Galerkin Approximations of the Stokes Problem with Applications to Fluid–Structure Interaction Problems
Paola F. Antonietti, Lorenzo Mascotto, Marco Verani and Stefano Zonca
Journal of Scientific Computing 90 (1) (2022)
DOI: 10.1007/s10915-021-01695-6
See this article
A review on arbitrarily regular conforming virtual element methods for second- and higher-order elliptic partial differential equations
Paola F. Antonietti, Gianmarco Manzini, Simone Scacchi and Marco Verani
Mathematical Models and Methods in Applied Sciences 31 (14) 2825 (2021)
DOI: 10.1142/S0218202521500627
See this article
An Lp spaces-based mixed virtual element method for the two-dimensional Navier–Stokes equations
Gabriel N. Gatica and Filánder A. Sequeira
Mathematical Models and Methods in Applied Sciences 31 (14) 2937 (2021)
DOI: 10.1142/S0218202521500664
See this article
Robust and scalable adaptive BDDC preconditioners for virtual element discretizations of elliptic partial differential equations in mixed form
Franco Dassi, Stefano Zampini and S. Scacchi
Computer Methods in Applied Mechanics and Engineering 391 114620 (2022)
DOI: 10.1016/j.cma.2022.114620
See this article
A formal construction of a divergence-free basis in the nonconforming virtual element method for the Stokes problem
Do Y. Kwak and Hyeokjoo Park
Numerical Algorithms 91 (1) 449 (2022)
DOI: 10.1007/s11075-022-01269-z
See this article
A mixed virtual element method for nearly incompressible linear elasticity equations
Huoyuan Duan and Ziliang Li
Advances in Computational Mathematics 49 (1) (2023)
DOI: 10.1007/s10444-023-10013-7
See this article
Nonconforming virtual element methods for the fourth-order variational inequalities of the first kind
Jiali Qiu, Jikun Zhao and Fei Wang
Journal of Computational and Applied Mathematics 425 115025 (2023)
DOI: 10.1016/j.cam.2022.115025
See this article
A Morley-type virtual element approximation for a wind-driven ocean circulation model on polygonal meshes
D. Adak, D. Mora and A. Silgado
Journal of Computational and Applied Mathematics 425 115026 (2023)
DOI: 10.1016/j.cam.2022.115026
See this article
Theoretical analysis and construction of numerical method for solving the Navier–Stokes equations in rotation form with corner singularity
Viktor A. Rukavishnikov and Alexey V. Rukavishnikov
Journal of Computational and Applied Mathematics 429 115218 (2023)
DOI: 10.1016/j.cam.2023.115218
See this article
The virtual element method for the 3D resistive magnetohydrodynamic model
Lourenço Beirão da Veiga, Franco Dassi, Gianmarci Manzini and Lorenzo Mascotto
Mathematical Models and Methods in Applied Sciences 33 (03) 643 (2023)
DOI: 10.1142/S021820252350015X
See this article
The divergence‐free nonconforming virtual element method for the
Navier–Stokes
problem
Bei Zhang, Jikun Zhao and Meng Li
Numerical Methods for Partial Differential Equations 39 (3) 1977 (2023)
DOI: 10.1002/num.22812
See this article
Artificial Compressibility Methods for the Incompressible Navier–Stokes Equations Using Lowest-Order Face-Based Schemes on Polytopal Meshes
Riccardo Milani, Jérôme Bonelle and Alexandre Ern
Computational Methods in Applied Mathematics 22 (1) 133 (2022)
DOI: 10.1515/cmam-2021-0089
See this article
The interior penalty virtual element method for the biharmonic problem
Jikun Zhao, Shipeng Mao, Bei Zhang and Fei Wang
Mathematics of Computation 92 (342) 1543 (2023)
DOI: 10.1090/mcom/3828
See this article
Unconditional Error Analysis of a Linearized Bdf2 Virtual Element Method for Nonlinear Ginzburg-Landau Equation with Variable Time Step
Nan Wang and Meng Li
SSRN Electronic Journal (2022)
DOI: 10.2139/ssrn.4098832
See this article
Optimal Error Estimates of Coupled and Divergence-Free Virtual Element Methods for the Poisson–Nernst–Planck/Navier–Stokes Equations and Applications in Electrochemical Systems
Mehdi Dehghan, Zeinab Gharibi and Ricardo Ruiz-Baier
Journal of Scientific Computing 94 (3) (2023)
DOI: 10.1007/s10915-023-02126-4
See this article
An arbitrary-order fully discrete Stokes complex on general polyhedral meshes
Marien-Lorenzo Hanot
Mathematics of Computation 92 (343) 1977 (2023)
DOI: 10.1090/mcom/3837
See this article
Lourenco Beirão da Veiga and Giuseppe Vacca
51 (2022)
DOI: 10.1007/978-3-030-87312-7_6
See this article
The virtual element method for a 2D incompressible MHD system
S. Naranjo-Alvarez, L. Beirão da Veiga, V.A. Bokil, F. Dassi, V. Gyrya and G. Manzini
Mathematics and Computers in Simulation 211 301 (2023)
DOI: 10.1016/j.matcom.2023.03.029
See this article
A fully-discrete virtual element method for the nonstationary Boussinesq equations in stream-function form
L. Beirão da Veiga, D. Mora and A. Silgado
Computer Methods in Applied Mechanics and Engineering 408 115947 (2023)
DOI: 10.1016/j.cma.2023.115947
See this article
A hybrid high-order method for the Sobolev equation
Chun-Mei Xie, Min-Fu Feng and Yan Luo
Applied Numerical Mathematics 178 84 (2022)
DOI: 10.1016/j.apnum.2022.03.006
See this article
An extrapolated Crank-Nicolson virtual element scheme for the nematic liquid crystal flows
Guang-an Zou, Xuyang Wang and Jian Li
Advances in Computational Mathematics 49 (3) (2023)
DOI: 10.1007/s10444-023-10028-0
See this article
VIRTUAL ELEMENT APPROXIMATIONS FOR NON-STATIONARY NAVIER-STOKES EQUATIONS ON POLYGONAL MESHES
Nitesh Verma and Sarvesh Kumar
Journal of Applied Analysis & Computation 13 (3) 1155 (2023)
DOI: 10.11948/20210381
See this article
A fully mixed virtual element method for Darcy–Forchheimer miscible displacement of incompressible fluids appearing in porous media
Mehdi Dehghan and Zeinab Gharibi
IMA Journal of Numerical Analysis (2023)
DOI: 10.1093/imanum/drad023
See this article
Vorticity-stabilized virtual elements for the Oseen equation
L. Beirão da Veiga, F. Dassi and G. Vacca
Mathematical Models and Methods in Applied Sciences 31 (14) 3009 (2021)
DOI: 10.1142/S0218202521500688
See this article
On the locking-free three-field virtual element methods for Biot’s consolidation model in poroelasticity
Xialan Tang, Zhibin Liu, Baiju Zhang and Minfu Feng
ESAIM: Mathematical Modelling and Numerical Analysis 55 S909 (2021)
DOI: 10.1051/m2an/2020064
See this article
Unconditionally energy stable C0-virtual element scheme for solving generalized Swift-Hohenberg equation
Mehdi Dehghan, Zeinab Gharibi and Mohammad Reza Eslahchi
Applied Numerical Mathematics 178 304 (2022)
DOI: 10.1016/j.apnum.2022.03.013
See this article
Exploring high-order three dimensional virtual elements: Bases and stabilizations
F. Dassi and L. Mascotto
Computers & Mathematics with Applications 75 (9) 3379 (2018)
DOI: 10.1016/j.camwa.2018.02.005
See this article
Pressure-independent velocity error estimates for (Navier-)Stokes nonconforming virtual element discretization with divergence free
Xin Liu and Yufeng Nie
Numerical Algorithms 90 (2) 477 (2022)
DOI: 10.1007/s11075-021-01195-6
See this article
A new local projection stabilization virtual element method for the Oseen problem on polygonal meshes
Yang Li, Minfu Feng and Yan Luo
Advances in Computational Mathematics 48 (3) (2022)
DOI: 10.1007/s10444-022-09952-4
See this article
Mixed virtual element method for the Helmholtz transmission eigenvalue problem on polytopal meshes
Jian Meng, Gang Wang and Liquan Mei
IMA Journal of Numerical Analysis 43 (3) 1685 (2023)
DOI: 10.1093/imanum/drac019
See this article
Parallel solvers for virtual element discretizations of elliptic equations in mixed form
F. Dassi and S. Scacchi
Computers & Mathematics with Applications 79 (7) 1972 (2020)
DOI: 10.1016/j.camwa.2019.07.027
See this article
A mixed virtual element method for a pseudostress-based formulation of linear elasticity
Ernesto Cáceres, Gabriel N. Gatica and Filánder A. Sequeira
Applied Numerical Mathematics 135 423 (2019)
DOI: 10.1016/j.apnum.2018.09.003
See this article
Conforming virtual element approximations of the two-dimensional Stokes problem
Gianmarco Manzini and Annamaria Mazzia
Applied Numerical Mathematics 181 176 (2022)
DOI: 10.1016/j.apnum.2022.06.002
See this article
Arbitrary-order pressure-robust DDR and VEM methods for the Stokes problem on polyhedral meshes
Lourenço Beirão da Veiga, Franco Dassi, Daniele A. Di Pietro and Jérôme Droniou
Computer Methods in Applied Mechanics and Engineering 397 115061 (2022)
DOI: 10.1016/j.cma.2022.115061
See this article
Stabilization of the nonconforming virtual element method
S. Bertoluzza, G. Manzini, M. Pennacchio and D. Prada
Computers & Mathematics with Applications 116 25 (2022)
DOI: 10.1016/j.camwa.2021.10.009
See this article
BDDC Preconditioners for Divergence Free Virtual Element Discretizations of the Stokes Equations
Tommaso Bevilacqua and Simone Scacchi
Journal of Scientific Computing 92 (2) (2022)
DOI: 10.1007/s10915-022-01929-1
See this article
A unified analysis of fully mixed virtual element method for wormhole propagation arising in the petroleum engineering
Mehdi Dehghan and Zeinab Gharibi
Computers & Mathematics with Applications 121 30 (2022)
DOI: 10.1016/j.camwa.2022.06.004
See this article
Conforming and nonconforming VEMs for the fourth-order reaction–subdiffusion equation: a unified framework
Meng Li, Jikun Zhao, Chengming Huang and Shaochun Chen
IMA Journal of Numerical Analysis 42 (3) 2238 (2022)
DOI: 10.1093/imanum/drab030
See this article
Virtual element method on polyhedral meshes for bi-harmonic eigenvalues problems
Franco Dassi and Iván Velásquez
Computers & Mathematics with Applications 121 85 (2022)
DOI: 10.1016/j.camwa.2022.07.001
See this article
The nonconforming virtual element method for semilinear elliptic problems
Liuchao Xiao, Meng Zhou and Jikun Zhao
Applied Mathematics and Computation 433 127402 (2022)
DOI: 10.1016/j.amc.2022.127402
See this article
Penalty Virtual Element Method for the 3D Incompressible Flow on Polyhedron Mesh
Lulu Li, Haiyan Su and Yinnian He
Entropy 24 (8) 1129 (2022)
DOI: 10.3390/e24081129
See this article
Weakly imposed Dirichlet boundary conditions for 2D and 3D Virtual Elements
Silvia Bertoluzza, Micol Pennacchio and Daniele Prada
Computer Methods in Applied Mechanics and Engineering 400 115454 (2022)
DOI: 10.1016/j.cma.2022.115454
See this article
Error estimates for a vorticity-based velocity–stress formulation of the Stokes eigenvalue problem
Felipe Lepe, Gonzalo Rivera and Jesus Vellojin
Journal of Computational and Applied Mathematics 420 114798 (2023)
DOI: 10.1016/j.cam.2022.114798
See this article
Unconditional error analysis of a linearized BDF2 virtual element method for nonlinear Ginzburg–Landau equation with variable time step
Nan Wang and Meng Li
Communications in Nonlinear Science and Numerical Simulation 116 106889 (2023)
DOI: 10.1016/j.cnsns.2022.106889
See this article
Edoardo Artioli, Stefano de Miranda, Carlo Lovadina, Luca Patruno and Michele Visinoni
31 137 (2022)
DOI: 10.1007/978-3-030-95319-5_4
See this article
Long Chen and Xuehai Huang
31 93 (2022)
DOI: 10.1007/978-3-030-95319-5_3
See this article
Dibyendu Adak, M. Arrutselvi, E. Natarajan and S. Natarajan
31 59 (2022)
DOI: 10.1007/978-3-030-95319-5_2
See this article
David Mora and Alberth Silgado
31 321 (2022)
DOI: 10.1007/978-3-030-95319-5_8
See this article
Gabriel N. Gatica, Antonio Márquez and Salim Meddahi
31 227 (2022)
DOI: 10.1007/978-3-030-95319-5_6
See this article
Lourenço Beirão da Veiga and Giuseppe Vacca
31 185 (2022)
DOI: 10.1007/978-3-030-95319-5_5
See this article
Sebastian Naranjo Alvarez, Vrushali A. Bokil, Vitaliy Gyrya and Gianmarco Manzini
31 499 (2022)
DOI: 10.1007/978-3-030-95319-5_12
See this article
Adaptive and Frugal FETI-DP for Virtual Elements
Axel Klawonn, Martin Lanser and Adam Wasiak
Vietnam Journal of Mathematics 51 (1) 89 (2023)
DOI: 10.1007/s10013-022-00580-5
See this article
A priori and a posteriori error estimates for a virtual element method for the non-self-adjoint Steklov eigenvalue problem
Gang Wang, Jian Meng, Ying Wang and Liquan Mei
IMA Journal of Numerical Analysis 42 (4) 3675 (2022)
DOI: 10.1093/imanum/drab079
See this article
A Virtual Element Method for the Steklov Eigenvalue Problem Allowing Small Edges
Felipe Lepe, David Mora, Gonzalo Rivera and Iván Velásquez
Journal of Scientific Computing 88 (2) (2021)
DOI: 10.1007/s10915-021-01555-3
See this article
A lowest-order virtual element method for the Helmholtz transmission eigenvalue problem
Jian Meng, Gang Wang and Liquan Mei
Calcolo 58 (1) (2021)
DOI: 10.1007/s10092-020-00391-5
See this article
Virtual Element Methods for three-dimensional Hellinger-Reissner elastostatic problems
Carlo Lovadina and Michele Visinoni
Communications in Applied and Industrial Mathematics 13 (1) 57 (2022)
DOI: 10.2478/caim-2022-0005
See this article
VIRTUAL ELEMENT APPROXIMATIONS FOR TWO SPECIES MODEL OF THE ADVECTION-DIFFUSION-REACTION IN POROELASTIC MEDIA
Nitesh Verma and Sarvesh Kumar
Mathematical Modelling and Analysis 27 (4) 668 (2022)
DOI: 10.3846/mma.2022.15542
See this article
A Robust and Mass Conservative Virtual Element Method for Linear Three-field Poroelasticity
Jun Guo and Minfu Feng
Journal of Scientific Computing 92 (3) (2022)
DOI: 10.1007/s10915-022-01960-2
See this article
Virtual element method for the Navier–Stokes equation coupled with the heat equation
Paola F Antonietti, Giuseppe Vacca and Marco Verani
IMA Journal of Numerical Analysis (2022)
DOI: 10.1093/imanum/drac072
See this article
On the virtual element method for topology optimization of non-Newtonian fluid-flow problems
Miguel A. A. Suárez, Juan S. Romero, Anderson Pereira and Ivan F. M. Menezes
Engineering with Computers 38 (6) 5445 (2022)
DOI: 10.1007/s00366-022-01637-2
See this article
A pressure‐robust weak Galerkin finite element method for
Navier–Stokes
equations
Lin Mu
Numerical Methods for Partial Differential Equations 39 (3) 2327 (2023)
DOI: 10.1002/num.22969
See this article
Virtual element method for linear elastic clamped plate model
Xiaoqin Shen, Chen Wang, Qian Yang, Jikun Zhao and Zhiming Gao
Applied Numerical Mathematics 191 1 (2023)
DOI: 10.1016/j.apnum.2023.04.020
See this article
A Conforming Virtual Element Method Based on Unfitted Meshes for the Elliptic Interface Problem
Haimei Wang, Feng Wang, Jinru Chen and Haifeng Ji
Journal of Scientific Computing 96 (1) (2023)
DOI: 10.1007/s10915-023-02229-y
See this article
Mixed virtual element methods for elastodynamics with weak symmetry
Baiju Zhang, Yan Yang and Minfu Feng
Journal of Computational and Applied Mathematics 353 49 (2019)
DOI: 10.1016/j.cam.2018.12.020
See this article