The Hitchhiker's Guide to the Virtual Element Method
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Publication:5169487
DOI10.1142/S021820251440003XzbMath1291.65336WikidataQ57386700 ScholiaQ57386700MaRDI QIDQ5169487
Lourenco Beirão da Veiga, Franco Brezzi, Luisa Donatella Marini, Alessandro Russo
Publication date: 10 July 2014
Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)
Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis (65-01)
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Cites Work
- Equivalent projectors for virtual element methods
- \texttt{PolyMesher}: a general-purpose mesh generator for polygonal elements written in Matlab
- An improved monotone finite volume scheme for diffusion equation on polygonal meshes
- Virtual element methods for plate bending problems
- Numerical integration of polynomials and discontinuous functions on irregular convex polygons and polyhedrons
- Barycentric coordinates for polytopes
- Extended finite element method on polygonal and quadtree meshes
- A multilevel multiscale mimetic (M\(^3\)) method for two-phase flows in porous media
- Interpolation-free monotone finite volume method for diffusion equations on polygonal meshes
- Local flux mimetic finite difference methods
- A new discretization methodology for diffusion problems on generalized polyhedral meshes
- A rational finite element basis
- The effect of inner products for discrete vector fields on the accuracy of mimetic finite difference methods
- A natural extension of the conventional finite volume method into polygonal unstructured meshes for CFD application
- Mimetic discretizations of elliptic control problems
- A residual based error estimator for the mimetic finite difference method
- Virtual Elements for Linear Elasticity Problems
- Arbitrary-Order Nodal Mimetic Discretizations of Elliptic Problems on Polygonal Meshes
- A mimetic discretization method for linear elasticity
- Convergence Analysis of the Mimetic Finite Difference Method for Elliptic Problems
- Mimetic finite differences for elliptic problems
- Numerical integration over arbitrary polygonal domains based on Schwarz-Christoffel conformal mapping
- The Orthogonal Decomposition Theorems for Mimetic Finite Difference Methods
- New mixed finite element method on polygonal and polyhedral meshes
- Higher Order BEM-Based FEM on Polygonal Meshes
- BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS
- MIXED FINITE ELEMENT METHODS: IMPLEMENTATION WITH ONE UNKNOWN PER ELEMENT, LOCAL FLUX EXPRESSIONS, POSITIVITY, POLYGONAL MESHES, AND RELATIONS TO OTHER METHODS
- A UNIFIED APPROACH TO MIMETIC FINITE DIFFERENCE, HYBRID FINITE VOLUME AND MIXED FINITE VOLUME METHODS
- Convergence of the Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes
- Conforming polygonal finite elements
- A FAMILY OF MIMETIC FINITE DIFFERENCE METHODS ON POLYGONAL AND POLYHEDRAL MESHES
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