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

Annamaria Mazzia

Mathematics and Computers in Simulation (MATCOM), 2020, vol. 177, issue C, 63-85

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.

Keywords: Virtual element method; Diffusion problem; Anisotropy; Locking (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:177:y:2020:i:c:p:63-85

DOI: 10.1016/j.matcom.2020.04.006

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