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The Mixed Virtual Element Discretization for highly-anisotropic problems: the role of the boundary degrees of freedom

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arxiv 2307.16474 v1 pith:FUUIYUJM submitted 2023-07-31 math.NA cs.NA

Stefano Berrone , Stefano Scialò , Gioana Teora This is my paper · ORCID
classification math.NAcs.NA
keywords boundarydegreesfreedomdifferentdiffusionelementhighly-anisotropicmixed
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In this paper, we discuss the accuracy and the robustness of the mixed Virtual Element Methods when dealing with highly-anisotropic diffusion problems. In particular, we analyze the performances of different approaches which are characterized by different sets of both boundary and internal degrees of freedom in presence of a strong anisotropy of the diffusion tensor with constant or variable coefficients. A new definition of the boundary degrees of freedom is also proposed and tested.

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Cited by 1 Pith paper

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  1. Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow

    math.NA 2024-12 conditional novelty 6.0 of 10

    Spectral multiscale basis functions built from local anisotropic Laplacians give accurate coarse models and O(1) two-grid convergence for heat flow with anisotropy up to 10^12.

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