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Vem++, a c++ library to handle and play with the Virtual Element Method

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arxiv 2310.05748 v1 pith:YBOOUZWL submitted 2023-10-03 math.NA cs.NA

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The Virtual Element Method (VEM) is an extension of the Finite Element Method (FEM) used for handling polytopal meshes. This paper provides a brief introduction to the VEM for a two-dimensional Laplacian problem. Additionally, it highlights the differences between a VEM implementation and a FEM code, emphasising the main challenges associated with the VEM. Furthermore, this paper presents a possible approach to address these challenges: vem++, a c++ library specifically developed for working with VEM discretisation. The library is designed to handle various partial differential equations in two or three dimensions, arising from both academic and engineering problems. Its flexible design allows for the seamless integration of new features, such as novel polytopes' quadrature rules, solvers, and virtual element spaces.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Stability and interpolation estimates of Hellinger-Reissner virtual element spaces

    math.NA 2025-02 conditional novelty 7.0 of 10

    Rigorous stability and interpolation estimates for Hellinger-Reissner virtual elements with constants depending only on mesh aspect ratio and polynomial degree, plus numerical evidence that degenerate shapes degrade t...

  2. A robust finite element method for linearized magnetohydrodynamics on general domains

    math.NA 2025-06 conditional novelty 6.0 of 10

    A stabilized H(div)/H(curl) finite element scheme extends robust linearized MHD discretizations from convex to general non-convex domains with less regular solutions.

  3. Robust virtual element methods for 3D stress-assisted diffusion problems

    math.NA 2025-02 conditional novelty 6.0 of 10

    A 3D virtual element method for stress-assisted diffusion is constructed, analyzed for well-posedness and optimal convergence, and demonstrated on a battery lithiation example.

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