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Research Article | Open Access

The mixed virtual element discretization for highly-anisotropic problems: the role of the boundary degrees of freedom

Stefano Berrone, Stefano Scialò, Gioana Teora( )
Dipartimento di Scienze Matematiche "Giuseppe Luigi Lagrange", Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino, 10129, Italy
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Abstract

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 performance of different approaches which are characterized by different sets of both boundary and internal degrees of freedom in the 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.

Keywords

mixed VEMorthogonal polynomial basisstabilizationill-conditioningboundary degrees of freedomanisotropic diffusion

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Mathematics in Engineering
Volume 5 Issue 6,
December 2023
Pages 1-32
DOI: 10.3934/mine.2023099

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Cite this article:
Berrone S, Scialò S, Teora G. The mixed virtual element discretization for highly-anisotropic problems: the role of the boundary degrees of freedom. Mathematics in Engineering, 2023, 5(6): 1-32. https://doi.org/10.3934/mine.2023099

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Received: 30 June 2023
Revised: 22 September 2023
Accepted: 04 October 2023
Published: 15 December 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)