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mVEM: A MATLAB Software Package for the Virtual Element Methods

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arxiv 2204.01339 v1 pith:J3RBZ6NF submitted 2022-04-04 math.NA cs.MScs.NA

Yue Yu This is my paper · ORCID
classification math.NAcs.MScs.NA
keywords methodsmvempackagesoftwarevemselementimplementationmatlab
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This paper summarizes the development of mVEM, a MATLAB software package containing efficient and easy-following codes for various virtual element methods (VEMs) published in the literature. We explain in detail the numerical implementation of the mixed VEMs for the Darcy problem and the three-dimensional linear VEMs for the Poisson equation. For other model problems, we present the construction of the discrete methods and only provide the implementation of the elliptic projection matrices. Some mesh related functions are also given in the package, including the mesh generation and refinement in two or three dimensions. mVEM is free and open source software.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 8 citations worldwide. Full citation record

  1. The Neural Approximated Virtual Element Method for Elasticity Problems

    math.NA 2025-07 conditional novelty 5.0 of 10

    A neural network that approximates virtual element basis functions from boundary data yields a stabilization-free polygonal discretization that converges on linear and nonlinear elasticity benchmarks.

  2. POLYDIM: A C++ library for POLYtopal DIscretization Methods

    math.NA 2025-05 conditional novelty 4.0 of 10

    PolyDiM is a new open-source C++ library that implements Virtual Element and other polytopal discretizations for PDEs in 2D and 3D on complex meshes.

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