The Hitchhiker's Guide to the Virtual Element Method

被引:476
作者
da Veiga, L. Beirao [1 ]
Brezzi, F. [2 ,3 ]
Marini, L. D. [3 ,4 ]
Russo, A. [5 ]
机构
[1] Univ Milano Statale, Dipartimento Matemat, I-20133 Milan, Italy
[2] IUSS Pavia, I-27100 Pavia, Italy
[3] IMATI CNR, I-27100 Pavia, Italy
[4] Univ Pavia, Dipartimento Matemat, I-27100 Pavia, Italy
[5] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, I-20153 Milan, Italy
关键词
Virtual Element Method; polygonal meshes; polyhedral meshes; implementation guide; FINITE-DIFFERENCE METHODS; POLYGONAL MESHES; POLYHEDRAL MESHES; MIMETIC DISCRETIZATIONS; ELLIPTIC PROBLEMS; DIFFUSION-PROBLEMS; VOLUME METHOD; CONVERGENCE; PRINCIPLES;
D O I
10.1142/S021820251440003X
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We present the essential ingredients in the Virtual Element Method for a simple linear elliptic second-order problem. We emphasize its computer implementation, which will enable interested readers to readily implement the method.
引用
收藏
页码:1541 / 1573
页数:33
相关论文
共 39 条
  • [1] Equivalent projectors for virtual element methods
    Ahmad, B.
    Alsaedi, A.
    Brezzi, F.
    Marini, L. D.
    Russo, A.
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2013, 66 (03) : 376 - 391
  • [2] Mimetic Discretizations of Elliptic Control Problems
    Antonietti, Paola F.
    Bigoni, Nadia
    Verani, Marco
    [J]. JOURNAL OF SCIENTIFIC COMPUTING, 2013, 56 (01) : 14 - 27
  • [3] A displacement-based finite element formulation for general polyhedra using harmonic shape functions
    Bishop, J. E.
    [J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2014, 97 (01) : 1 - 31
  • [4] Bochev PB, 2006, IMA VOL MATH APPL, V142, P89
  • [5] Bonelle J., 2012, PREPRINT
  • [6] Convergence of the mimetic finite difference method for diffusion problems on polyhedral meshes
    Brezzi, F
    Lipnikov, K
    Shashkov, M
    [J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2005, 43 (05) : 1872 - 1896
  • [7] A family of mimetic finite difference methods on polygonal and polyhedral meshes
    Brezzi, F
    Lipnikov, K
    Simoncini, V
    [J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2005, 15 (10) : 1533 - 1551
  • [8] BASIC PRINCIPLES OF MIXED VIRTUAL ELEMENT METHODS
    Brezzi, F.
    Falk, Richard S.
    Marini, L. Donatella
    [J]. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2014, 48 (04): : 1227 - 1240
  • [9] A new discretization methodology for diffusion problems on generalized polyhedral meshes
    Brezzi, Franco
    Lipnikov, Konstantin
    Shashkov, Mikhail
    Simoncini, Valeria
    [J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2007, 196 (37-40) : 3682 - 3692
  • [10] Virtual Element Methods for plate bending problems
    Brezzi, Franco
    Marini, L. Donatella
    [J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2013, 253 : 455 - 462