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

Stefano Berrone; Stefano Scialò; Gioana Teora; Stefano Berrone; Stefano Scialò; Gioana Teora

doi:10.3934/mine.2023099

Mathematics in Engineering

2023, Volume 5, Issue 6: 1-32. doi: 10.3934/mine.2023099

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

Dipartimento di Scienze Matematiche "Giuseppe Luigi Lagrange", Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino, 10129, Italy

Received: 30 June 2023 Revised: 22 September 2023 Accepted: 04 October 2023 Published: 12 October 2023

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.
- mixed VEM,
- orthogonal polynomial basis,
- stabilization,
- ill-conditioning,
- boundary degrees of freedom,
- anisotropic diffusion
Citation: Stefano Berrone, Stefano Scialò, Gioana Teora. The mixed virtual element discretization for highly-anisotropic problems: the role of the boundary degrees of freedom[J]. Mathematics in Engineering, 2023, 5(6): 1-32. doi: 10.3934/mine.2023099

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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.

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