Mixed virtual element methods for general second order elliptic problems on polygonal meshes
ESAIM: M2AN, 50 3 (2016) 727-747
Published online: 2016-05-23
Articles citing this article
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:
This article has been cited by the following article(s):
Least‐squares virtual element method for the convection‐diffusion‐reaction problem
Gang Wang, Ying Wang and Yinnian HeInternational Journal for Numerical Methods in Engineering 122 (11) 2672 (2021)
https://doi.org/10.1002/nme.6636
Multiscale VEM for the Biot consolidation analysis of complex and highly heterogeneous domains
Abhilash Sreekumar, Savvas P. Triantafyllou, François-Xavier Bécot and Fabien ChevillotteComputer Methods in Applied Mechanics and Engineering 375 113543 (2021)
https://doi.org/10.1016/j.cma.2020.113543
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 VeraniMathematical Models and Methods in Applied Sciences 31 (14) 2825 (2021)
https://doi.org/10.1142/S0218202521500627
Comparison of the response to geometrical complexity of methods for unstationary simulations in discrete fracture networks with conforming, polygonal, and non-matching grids
Andrea Borio, Alessio Fumagalli and Stefano ScialòComputational Geosciences 25 (1) 143 (2021)
https://doi.org/10.1007/s10596-020-09996-9
A robust VEM-based approach for flow simulations in poro-fractured media
Stefano Berrone, Andrea Borio, Alessandro D’Auria, Stefano Scialò and Fabio ViciniMathematical Models and Methods in Applied Sciences 31 (14) 2855 (2021)
https://doi.org/10.1142/S0218202521500639
Polyhedral Methods in Geosciences
Alessio Fumagalli, Anna Scotti and Luca FormaggiaSEMA SIMAI Springer Series, Polyhedral Methods in Geosciences 27 299 (2021)
https://doi.org/10.1007/978-3-030-69363-3_8
On the locking-free three-field virtual element methods for Biot’s consolidation model in poroelasticity
Xialan Tang, Zhibin Liu, Baiju Zhang and Minfu FengESAIM: Mathematical Modelling and Numerical Analysis 55 S909 (2021)
https://doi.org/10.1051/m2an/2020064
A priori error analysis for a mixed VEM discretization of the spectral problem for the Laplacian operator
Felipe Lepe and Gonzalo RiveraCalcolo 58 (2) (2021)
https://doi.org/10.1007/s10092-021-00412-x
A posteriori error analysis of a mixed virtual element method for a nonlinear Brinkman model of porous media flow
Mauricio Munar and Filánder A. SequeiraComputers & Mathematics with Applications 80 (5) 1240 (2020)
https://doi.org/10.1016/j.camwa.2020.06.005
Bricks for the mixed high-order virtual element method: Projectors and differential operators
F. Dassi and G. VaccaApplied Numerical Mathematics 155 140 (2020)
https://doi.org/10.1016/j.apnum.2019.03.014
A virtual element method for the Laplacian eigenvalue problem in mixed form
Jian Meng, Yongchao Zhang and Liquan MeiApplied Numerical Mathematics 156 1 (2020)
https://doi.org/10.1016/j.apnum.2020.03.026
A Posteriori Error Estimates for the Virtual Element Method for the Stokes Problem
Gang Wang, Ying Wang and Yinnian HeJournal of Scientific Computing 84 (2) (2020)
https://doi.org/10.1007/s10915-020-01281-2
Parallel block preconditioners for three-dimensional virtual element discretizations of saddle-point problems
F. Dassi and S. ScacchiComputer Methods in Applied Mechanics and Engineering 372 113424 (2020)
https://doi.org/10.1016/j.cma.2020.113424
A mixed virtual element method for the vibration problem of clamped Kirchhoff plate
Jian Meng and Liquan MeiAdvances in Computational Mathematics 46 (5) (2020)
https://doi.org/10.1007/s10444-020-09810-1
A New Projection-Based Stabilized Virtual Element Method for the Stokes Problem
Jun Guo and Minfu FengJournal of Scientific Computing 85 (1) (2020)
https://doi.org/10.1007/s10915-020-01301-1
The Hybrid High-Order Method for Polytopal Meshes
Daniele Antonio Di Pietro and Jérôme DroniouMS&A, The Hybrid High-Order Method for Polytopal Meshes 19 83 (2020)
https://doi.org/10.1007/978-3-030-37203-3_3
Virtual element methods for nonlocal parabolic problems on general type of meshes
D. Adak and S. NatarajanAdvances in Computational Mathematics 46 (5) (2020)
https://doi.org/10.1007/s10444-020-09811-0
Parallel solvers for virtual element discretizations of elliptic equations in mixed form
F. Dassi and S. ScacchiComputers & Mathematics with Applications 79 (7) 1972 (2020)
https://doi.org/10.1016/j.camwa.2019.07.027
A high-order discontinuous Galerkin approach to the elasto-acoustic problem
Paola F. Antonietti, Francesco Bonaldi and Ilario MazzieriComputer Methods in Applied Mechanics and Engineering 358 112634 (2020)
https://doi.org/10.1016/j.cma.2019.112634
A low-order locking-free virtual element for linear elasticity problems
Xialan Tang, Zhibin Liu, Baiju Zhang and Minfu FengComputers & Mathematics with Applications 80 (5) 1260 (2020)
https://doi.org/10.1016/j.camwa.2020.04.032
A least-squares virtual element method for second-order elliptic problems
Ying Wang and Gang WangComputers & Mathematics with Applications 80 (8) 1873 (2020)
https://doi.org/10.1016/j.camwa.2020.08.023
Sharp algebraic and total a posteriori error bounds for h and p finite elements via a multilevel approach. Recovering mass balance in any situation
Jan Papež, Ulrich Rüde, Martin Vohralík and Barbara WohlmuthComputer Methods in Applied Mechanics and Engineering 371 113243 (2020)
https://doi.org/10.1016/j.cma.2020.113243
FETI-DP for the Three Dimensional Virtual Element Method
Silvia Bertoluzza, Micol Pennacchio and Daniele PradaSIAM Journal on Numerical Analysis 58 (3) 1556 (2020)
https://doi.org/10.1137/18M1233303
Unified analysis of discontinuous Galerkin approximations of flows in fractured porous media on polygonal and polyhedral grids
Paola F. Antonietti, Chiara Facciolà and Marco VeraniMathematics in Engineering 2 (2) 340 (2020)
https://doi.org/10.3934/mine.2020017
Conforming, non-conforming and non-matching discretization couplings in discrete fracture network simulations
Alessio Fumagalli, Eirik Keilegavlen and Stefano ScialòJournal of Computational Physics 376 694 (2019)
https://doi.org/10.1016/j.jcp.2018.09.048
Convergence analysis of virtual element methods for semilinear parabolic problems on polygonal meshes
Dibyendu Adak, E. Natarajan and Sarvesh KumarNumerical Methods for Partial Differential Equations 35 (1) 222 (2019)
https://doi.org/10.1002/num.22298
A Fully Computable A Posteriori Error Estimate for the Stokes Equations on Polytopal Meshes
Feng Bao, Lin Mu and Jin WangSIAM Journal on Numerical Analysis 57 (1) 458 (2019)
https://doi.org/10.1137/18M1171515
Weak Galerkin based a posteriori error estimates for second order elliptic interface problems on polygonal meshes
Lin MuJournal of Computational and Applied Mathematics 361 413 (2019)
https://doi.org/10.1016/j.cam.2019.04.026
A mixed discretization of elliptic problems on polyhedra using anisotropic hybrid meshes
Alexis B. Jawtuschenko and Ariel L. LombardiCalcolo 56 (2) (2019)
https://doi.org/10.1007/s10092-019-0303-x
Numerical Mathematics and Advanced Applications ENUMATH 2017
Eirik Keilegavlen, Alessio Fumagalli, Runar Berge and Ivar StefanssonLecture Notes in Computational Science and Engineering, Numerical Mathematics and Advanced Applications ENUMATH 2017 126 573 (2019)
https://doi.org/10.1007/978-3-319-96415-7_52
Mixed virtual element methods for elastodynamics with weak symmetry
Baiju Zhang, Yan Yang and Minfu FengJournal of Computational and Applied Mathematics 353 49 (2019)
https://doi.org/10.1016/j.cam.2018.12.020
A high-order mixed polygonal finite element for incompressible Stokes flow analysis
T. Vu-Huu, C. Le-Thanh, H. Nguyen-Xuan and M. Abdel-WahabComputer Methods in Applied Mechanics and Engineering 356 175 (2019)
https://doi.org/10.1016/j.cma.2019.07.005
Numerical solution of fluid-structure interaction problems by means of a high order Discontinuous Galerkin method on polygonal grids
Paola Antonietti, Marco Verani, Christian Vergara and Stefano ZoncaFinite Elements in Analysis and Design 159 1 (2019)
https://doi.org/10.1016/j.finel.2019.02.002
A mixed virtual element method for a pseudostress-based formulation of linear elasticity
Ernesto Cáceres, Gabriel N. Gatica and Filánder A. SequeiraApplied Numerical Mathematics 135 423 (2019)
https://doi.org/10.1016/j.apnum.2018.09.003
Dual Virtual Element Methods for Discrete Fracture Matrix models
Alessio Fumagalli, Eirik Keilegavlen, A. Anciaux-Sedrakian and Q. H. TranOil & Gas Science and Technology – Revue d’IFP Energies nouvelles 74 41 (2019)
https://doi.org/10.2516/ogst/2019008
A priori and a posterior error estimate of new weak Galerkin finite element methods for second order elliptic interface problems on polygonal meshes
Lin MuJournal of Computational and Applied Mathematics 362 423 (2019)
https://doi.org/10.1016/j.cam.2018.09.007
Stabilized virtual element methods for the unsteady incompressible Navier–Stokes equations
Diego Irisarri and Guillermo HaukeCalcolo 56 (4) (2019)
https://doi.org/10.1007/s10092-019-0332-5
A mixed virtual element method for a nonlinear Brinkman model of porous media flow
Gabriel N. Gatica, Mauricio Munar and Filánder A. SequeiraCalcolo 55 (2) (2018)
https://doi.org/10.1007/s10092-018-0262-7
High-order Discontinuous Galerkin methods for the elastodynamics equation on polygonal and polyhedral meshes
P.F. Antonietti and I. MazzieriComputer Methods in Applied Mechanics and Engineering 342 414 (2018)
https://doi.org/10.1016/j.cma.2018.08.012
Virtual element method for two-dimensional linear elasticity problem in mixed weakly symmetric formulation
Baiju Zhang and Minfu FengApplied Mathematics and Computation 328 1 (2018)
https://doi.org/10.1016/j.amc.2018.01.023
A simple a posteriori estimate on general polytopal meshes with applications to complex porous media flows
Martin Vohralík and Soleiman YousefComputer Methods in Applied Mechanics and Engineering 331 728 (2018)
https://doi.org/10.1016/j.cma.2017.11.027
Virtual element method for second-order elliptic eigenvalue problems
Francesca Gardini and Giuseppe VaccaIMA Journal of Numerical Analysis 38 (4) 2026 (2018)
https://doi.org/10.1093/imanum/drx063
Unified formulation and analysis of mixed and primal discontinuous skeletal methods on polytopal meshes
Daniele Boffi and Daniele A. Di PietroESAIM: Mathematical Modelling and Numerical Analysis 52 (1) 1 (2018)
https://doi.org/10.1051/m2an/2017036
Fast Numerical Integration on Polytopic Meshes with Applications to Discontinuous Galerkin Finite Element Methods
Paola F. Antonietti, Paul Houston and Giorgio PennesiJournal of Scientific Computing 77 (3) 1339 (2018)
https://doi.org/10.1007/s10915-018-0802-y
The fully nonconforming virtual element method for biharmonic problems
P. F. Antonietti, G. Manzini and M. VeraniMathematical Models and Methods in Applied Sciences 28 (02) 387 (2018)
https://doi.org/10.1142/S0218202518500100
Virtual Elements for the Reissner‐Mindlin plate problem
Claudia ChinosiNumerical Methods for Partial Differential Equations 34 (4) 1117 (2018)
https://doi.org/10.1002/num.22248
Ill‐conditioning in the virtual element method: Stabilizations and bases
Lorenzo MascottoNumerical Methods for Partial Differential Equations 34 (4) 1258 (2018)
https://doi.org/10.1002/num.22257
A mixed virtual element method for the Navier–Stokes equations
Gabriel N. Gatica, Mauricio Munar and Filánder A. SequeiraMathematical Models and Methods in Applied Sciences 28 (14) 2719 (2018)
https://doi.org/10.1142/S0218202518500598
Dual virtual element method in presence of an inclusion
Alessio FumagalliApplied Mathematics Letters 86 22 (2018)
https://doi.org/10.1016/j.aml.2018.06.004
A multigrid algorithm for the p-version of the virtual element method
Paola F. Antonietti, Lorenzo Mascotto and Marco VeraniESAIM: Mathematical Modelling and Numerical Analysis 52 (1) 337 (2018)
https://doi.org/10.1051/m2an/2018007
An H1-conforming virtual element for Darcy and Brinkman equations
Giuseppe VaccaMathematical Models and Methods in Applied Sciences 28 (01) 159 (2018)
https://doi.org/10.1142/S0218202518500057
SUPG stabilization for the nonconforming virtual element method for advection–diffusion–reaction equations
S. Berrone, A. Borio and G. ManziniComputer Methods in Applied Mechanics and Engineering 340 500 (2018)
https://doi.org/10.1016/j.cma.2018.05.027
A Mixed Virtual Element Method for Quasi-Newtonian Stokes Flows
Ernesto Cáceres, Gabriel N. Gatica and Filánder A. SequeiraSIAM Journal on Numerical Analysis 56 (1) 317 (2018)
https://doi.org/10.1137/17M1121160
Dual Virtual Element Method for Discrete Fractures Networks
Alessio Fumagalli and Eirik KeilegavlenSIAM Journal on Scientific Computing 40 (1) B228 (2018)
https://doi.org/10.1137/16M1098231
Some Estimates for Virtual Element Methods
Susanne C. Brenner, Qingguang Guan and Li-Yeng SungComputational Methods in Applied Mathematics 17 (4) 553 (2017)
https://doi.org/10.1515/cmam-2017-0008
A mixed virtual element method for the Brinkman problem
Ernesto Cáceres, Gabriel N. Gatica and Filánder A. SequeiraMathematical Models and Methods in Applied Sciences 27 (04) 707 (2017)
https://doi.org/10.1142/S0218202517500142
Multigrid algorithms for $$\varvec{hp}$$ h p -version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes
P. F. Antonietti, P. Houston, X. Hu, M. Sarti and M. VeraniCalcolo 54 (4) 1169 (2017)
https://doi.org/10.1007/s10092-017-0223-6
Mixed Virtual Elements for discrete fracture network simulations
Matías Fernando Benedetto, Andrea Borio and Stefano ScialòFinite Elements in Analysis and Design 134 55 (2017)
https://doi.org/10.1016/j.finel.2017.05.011
A virtual element method for the acoustic vibration problem
Lourenço Beirão da Veiga, David Mora, Gonzalo Rivera and Rodolfo RodríguezNumerische Mathematik 136 (3) 725 (2017)
https://doi.org/10.1007/s00211-016-0855-5
BDDC and FETI-DP for the virtual element method
Silvia Bertoluzza, Micol Pennacchio and Daniele PradaCalcolo 54 (4) 1565 (2017)
https://doi.org/10.1007/s10092-017-0242-3
On the virtual element method for topology optimization on polygonal meshes: A numerical study
P.F. Antonietti, M. Bruggi, S. Scacchi and M. VeraniComputers & Mathematics with Applications 74 (5) 1091 (2017)
https://doi.org/10.1016/j.camwa.2017.05.025
Convergence Analysis of the mimetic Finite Difference Method for Elliptic Problems with Staggered Discretizations of Diffusion Coefficients
G. Manzini, K. Lipnikov, J. D. Moulton and M. ShashkovSIAM Journal on Numerical Analysis 55 (6) 2956 (2017)
https://doi.org/10.1137/16M1108479
Preface
L. Beirão da Veiga and A. ErnESAIM: Mathematical Modelling and Numerical Analysis 50 (3) 633 (2016)
https://doi.org/10.1051/m2an/2016034
A plane wave virtual element method for the Helmholtz problem
Ilaria Perugia, Paola Pietra and Alessandro RussoESAIM: Mathematical Modelling and Numerical Analysis 50 (3) 783 (2016)
https://doi.org/10.1051/m2an/2015066
Virtual Element Method for fourth order problems: L2-estimates
Claudia Chinosi and L. Donatella MariniComputers & Mathematics with Applications 72 (8) 1959 (2016)
https://doi.org/10.1016/j.camwa.2016.02.001
Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations
Lourenco Beirão da Veiga, Franco Brezzi, Luisa Donatella Marini and Alessandro RussoLecture Notes in Computational Science and Engineering, Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations 114 39 (2016)
https://doi.org/10.1007/978-3-319-41640-3_2