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A numerical study of the virtual element method in anisotropic diffusion problems

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  • Mazzia, Annamaria

Abstract

In this paper, we present the Virtual Element Method (VEM) for the solution of strongly anisotropic diffusion equations. In the VEM, the bilinear form associated with the diffusion equations is decomposed into two parts: a consistency term and a stability term. Therefore, the local stiffness matrix is the sum of two matrices: a consistency matrix and a stability matrix. Both matrices are constructed by using suitable projection operators that are computable from the degrees of freedom. The VEM stiffness matrix becomes very ill-conditioned in presence of a strong anisotropy of the diffusion tensor coefficient, leading to a loss of convergence, an effect known in the literature as mesh locking.

Suggested Citation

  • Mazzia, Annamaria, 2020. "A numerical study of the virtual element method in anisotropic diffusion problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 63-85.
    • Handle: RePEc:eee:matcom:v:177:y:2020:i:c:p:63-85
    DOI: 10.1016/j.matcom.2020.04.006
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    Cited by:

    1. Cuevas, Erik & Becerra, Héctor & Luque, Alberto, 2021. "Anisotropic diffusion filtering through multi-objective optimization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 410-429.

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