A virtual element method for the vibration problem of Kirchhoff plates
ESAIM: M2AN, 52 4 (2018) 1437-1456
Published online: 2018-09-28
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):
The multigrid discretization of mixed discontinuous Galerkin method for the biharmonic eigenvalue problem
Jinhua Feng, Shixi Wang, Hai Bi and Yidu YangMathematical Methods in the Applied Sciences 48 (2) 2635 (2025)
https://doi.org/10.1002/mma.10455
VEM approximation for the Stokes eigenvalue problem: A priori and a posteriori error analysis
Dibyendu Adak, Felipe Lepe and Gonzalo RiveraComputer Methods in Applied Mechanics and Engineering 444 118156 (2025)
https://doi.org/10.1016/j.cma.2025.118156
Virtual element method for the Laplacian eigenvalue problem with Neumann boundary conditions
Junchi Ma, Lin Chen and Xinbo ChengAIMS Mathematics 10 (4) 8203 (2025)
https://doi.org/10.3934/math.2025377
On the stabilization of a virtual element method for an acoustic vibration problem
Linda Alzaben, Daniele Boffi, Andreas Dedner and Lucia GastaldiMathematical Models and Methods in Applied Sciences 35 (03) 655 (2025)
https://doi.org/10.1142/S0218202525500071
Adaptive mixed virtual element method for the fourth-order singularly perturbed problem
Jian Meng, Xu Qian, Jiali Qiu and Jingmin XiaJournal of Computational Physics 524 113738 (2025)
https://doi.org/10.1016/j.jcp.2025.113738
A Stabilization-Free Virtual Element Method for the Convection–Diffusion Eigenproblem
Francesca Marcon and David MoraJournal of Scientific Computing 102 (2) (2025)
https://doi.org/10.1007/s10915-024-02765-1
The interior penalty virtual element method for the two-dimensional biharmonic eigenvalue problem
Jian Meng, Bing-Bing Xu, Fang Su and Xu QianComputer Methods in Applied Mechanics and Engineering 436 117685 (2025)
https://doi.org/10.1016/j.cma.2024.117685
H1-conforming virtual element method for the Laplacian eigenvalue problem in mixed form
Jian Meng, Liquan Mei and Mingfa FeiJournal of Computational and Applied Mathematics 436 115395 (2024)
https://doi.org/10.1016/j.cam.2023.115395
Morley type virtual element method for von Kármán equations
Devika Shylaja and Sarvesh KumarAdvances in Computational Mathematics 50 (5) (2024)
https://doi.org/10.1007/s10444-024-10158-z
Virtual element methods for Biot–Kirchhoff poroelasticity
Rekha Khot, David Mora and Ricardo Ruiz-BaierMathematics of Computation (2024)
https://doi.org/10.1090/mcom/3983
Nonconforming virtual element methods for velocity-pressure Stokes eigenvalue problem
Dibyendu Adak, Gianmarco Manzini and Sundararajan NatarajanApplied Numerical Mathematics 202 42 (2024)
https://doi.org/10.1016/j.apnum.2024.04.009
A multi-level correction scheme for biharmonic eigenvalue problem by nonconforming finite element method
Xi Yingxia, Xie Hehu and Ji XiaSCIENTIA SINICA Mathematica (2024)
https://doi.org/10.1360/SCM-2022-0215
395 (2024)
https://doi.org/10.1007/978-3-031-39255-9_13
Mixed virtual element method for the Helmholtz transmission eigenvalue problem on polytopal meshes
Jian Meng, Gang Wang and Liquan MeiIMA Journal of Numerical Analysis 43 (3) 1685 (2023)
https://doi.org/10.1093/imanum/drac019
Virtual element formulation for gradient elasticity
Peter Wriggers and Blaž HudobivnikActa Mechanica Sinica 39 (4) (2023)
https://doi.org/10.1007/s10409-022-22306-x
Nonconforming virtual element discretization for the transmission eigenvalue problem
Dibyendu Adak, David Mora and Iván VelásquezComputers & Mathematics with Applications 152 250 (2023)
https://doi.org/10.1016/j.camwa.2023.10.032
A C0-nonconforming virtual element methods for the vibration and buckling problems of thin plates
Dibyendu Adak, David Mora and Iván VelásquezComputer Methods in Applied Mechanics and Engineering 403 115763 (2023)
https://doi.org/10.1016/j.cma.2022.115763
Virtual element method for linear elastic clamped plate model
Xiaoqin Shen, Chen Wang, Qian Yang, Jikun Zhao and Zhiming GaoApplied Numerical Mathematics 191 1 (2023)
https://doi.org/10.1016/j.apnum.2023.04.020
137 3 (2023)
https://doi.org/10.1007/978-3-031-20432-6_1
On two simple virtual Kirchhoff-Love plate elements for isotropic and anisotropic materials
P. Wriggers, B. Hudobivnik and O. AllixComputational Mechanics 69 (2) 615 (2022)
https://doi.org/10.1007/s00466-021-02106-1
Virtual element method on polyhedral meshes for bi-harmonic eigenvalues problems
Franco Dassi and Iván VelásquezComputers & Mathematics with Applications 121 85 (2022)
https://doi.org/10.1016/j.camwa.2022.07.001
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 SilgadoIMA Journal of Numerical Analysis 42 (4) 3632 (2022)
https://doi.org/10.1093/imanum/drab078
The optimal order convergence for the lowest order mixed finite element method of the biharmonic eigenvalue problem
Jian Meng and Liquan MeiJournal of Computational and Applied Mathematics 402 113783 (2022)
https://doi.org/10.1016/j.cam.2021.113783
The Virtual Element Method and its Applications
Daniele Boffi, Francesca Gardini and Lucia GastaldiSEMA SIMAI Springer Series, The Virtual Element Method and its Applications 31 275 (2022)
https://doi.org/10.1007/978-3-030-95319-5_7
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 MeiIMA Journal of Numerical Analysis 42 (4) 3675 (2022)
https://doi.org/10.1093/imanum/drab079
The Virtual Element Method and its Applications
Paola F. Antonietti, Gianmarco Manzini, Ilario Mazzieri, Simone Scacchi and Marco VeraniSEMA SIMAI Springer Series, The Virtual Element Method and its Applications 31 411 (2022)
https://doi.org/10.1007/978-3-030-95319-5_10
Virtual element method for the Helmholtz transmission eigenvalue problem of anisotropic media
Jian Meng and Liquan MeiMathematical Models and Methods in Applied Sciences 32 (08) 1493 (2022)
https://doi.org/10.1142/S0218202522500348
On a virtual element formulation for trusses and beams
P. WriggersArchive of Applied Mechanics 92 (6) 1655 (2022)
https://doi.org/10.1007/s00419-022-02113-5
A $$C^1$$–$$C^0$$ virtual element discretization for a sixth-order elliptic equation
José Causil, Carlos Reales and Iván VelásquezCalcolo 59 (4) (2022)
https://doi.org/10.1007/s10092-022-00482-5
Free vibration of FGM Mindlin plates submerged in fluid
Hui-Cui Li, Liao-Liang Ke, Zhang-Ming Wu and Jie YangEngineering Structures 259 114144 (2022)
https://doi.org/10.1016/j.engstruct.2022.114144
Convergence Analysis of Virtual Element Method for Nonlinear Nonlocal Dynamic Plate Equation
D. Adak, D. Mora and S. NatarajanJournal of Scientific Computing 91 (1) (2022)
https://doi.org/10.1007/s10915-022-01794-y
A C1 virtual element method for the stationary quasi-geostrophic equations of the ocean
David Mora and Alberth SilgadoComputers & Mathematics with Applications 116 212 (2022)
https://doi.org/10.1016/j.camwa.2021.05.022
$ C^1 $-VEM for some variants of the Cahn-Hilliard equation: A numerical exploration
Paola F. Antonietti, Simone Scacchi, Giuseppe Vacca and Marco VeraniDiscrete and Continuous Dynamical Systems - S 15 (8) 1919 (2022)
https://doi.org/10.3934/dcdss.2022038
A lowest-order free-stabilization Virtual Element Method for the Laplacian eigenvalue problem
Jian Meng, Xue Wang, Linlin Bu and Liquan MeiJournal of Computational and Applied Mathematics 410 114013 (2022)
https://doi.org/10.1016/j.cam.2021.114013
A virtual element method for the von Kármán equations
Carlo Lovadina, David Mora and Iván VelásquezESAIM: Mathematical Modelling and Numerical Analysis 55 (2) 533 (2021)
https://doi.org/10.1051/m2an/2020085
A lowest-order virtual element method for the Helmholtz transmission eigenvalue problem
Jian Meng, Gang Wang and Liquan MeiCalcolo 58 (1) (2021)
https://doi.org/10.1007/s10092-020-00391-5
A $$C^{1}-C^{0}$$ conforming virtual element discretization for the transmission eigenvalue problem
David Mora and Iván VelásquezResearch in the Mathematical Sciences 8 (4) (2021)
https://doi.org/10.1007/s40687-021-00291-2
A virtual element discretization for the time dependent Navier–Stokes equations in stream-function formulation
Dibyendu Adak, David Mora, Sundararajan Natarajan and Alberth SilgadoESAIM: Mathematical Modelling and Numerical Analysis 55 (5) 2535 (2021)
https://doi.org/10.1051/m2an/2021058
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
Virtual Elements for the Transmission Eigenvalue Problem on Polytopal Meshes
David Mora and Iván VelásquezSIAM Journal on Scientific Computing 43 (4) A2425 (2021)
https://doi.org/10.1137/20M1347887
A C0 virtual element method for the biharmonic eigenvalue problem
Jian Meng and Liquan MeiInternational Journal of Computer Mathematics 98 (9) 1821 (2021)
https://doi.org/10.1080/00207160.2020.1849635
A dual hybrid virtual element method for plane elasticity problems
Edoardo Artioli, Stefano de Miranda, Carlo Lovadina and Luca PatrunoESAIM: Mathematical Modelling and Numerical Analysis 54 (5) 1725 (2020)
https://doi.org/10.1051/m2an/2020011
Virtual element method (VEM)-based topology optimization: an integrated framework
Heng Chi, Anderson Pereira, Ivan F. M. Menezes and Glaucio H. PaulinoStructural and Multidisciplinary Optimization 62 (3) 1089 (2020)
https://doi.org/10.1007/s00158-019-02268-w
A C1 Virtual Element Method on polyhedral meshes
L. Beirão da Veiga, F. Dassi and A. RussoComputers & Mathematics with Applications 79 (7) 1936 (2020)
https://doi.org/10.1016/j.camwa.2019.06.019
A virtual element method for a nonlocal FitzHugh–Nagumo model of cardiac electrophysiology
Mauricio Sepúlveda, David Mora, Mostafa Bendahmane and Verónica AnayaIMA Journal of Numerical Analysis 40 (2) 1544 (2020)
https://doi.org/10.1093/imanum/drz001
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
Virtual element for the buckling problem of Kirchhoff–Love plates
David Mora and Iván VelásquezComputer Methods in Applied Mechanics and Engineering 360 112687 (2020)
https://doi.org/10.1016/j.cma.2019.112687
Approximation of PDE eigenvalue problems involving parameter dependent matrices
Daniele Boffi, Francesca Gardini and Lucia GastaldiCalcolo 57 (4) (2020)
https://doi.org/10.1007/s10092-020-00390-6
The p- and hp-versions of the virtual element method for elliptic eigenvalue problems
O. Čertík, F. Gardini, G. Manzini, L. Mascotto and G. VaccaComputers & Mathematics with Applications 79 (7) 2035 (2020)
https://doi.org/10.1016/j.camwa.2019.10.018
A linear virtual element method for the Kirchhoff plate buckling problem
Jian Meng and Liquan MeiApplied Mathematics Letters 103 106188 (2020)
https://doi.org/10.1016/j.aml.2019.106188
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 priori and a posteriori error estimates for a virtual element spectral analysis for the elasticity equations
David Mora and Gonzalo RiveraIMA Journal of Numerical Analysis 40 (1) 322 (2020)
https://doi.org/10.1093/imanum/dry063
The Stokes Complex for Virtual Elements with Application to Navier–Stokes Flows
L. Beirão da Veiga, D. Mora and G. VaccaJournal of Scientific Computing 81 (2) 990 (2019)
https://doi.org/10.1007/s10915-019-01049-3
A virtual element method for a biharmonic Steklov eigenvalue problem
Gabriel MonzónAdvances in Pure and Applied Mathematics 10 (4) 325 (2019)
https://doi.org/10.1515/apam-2018-0072
The nonconforming Virtual Element Method for eigenvalue problems
Francesca Gardini, Gianmarco Manzini and Giuseppe VaccaESAIM: Mathematical Modelling and Numerical Analysis 53 (3) 749 (2019)
https://doi.org/10.1051/m2an/2018074
A virtual element method for the transmission eigenvalue problem
David Mora and Iván VelásquezMathematical Models and Methods in Applied Sciences 28 (14) 2803 (2018)
https://doi.org/10.1142/S0218202518500616