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Borio, Andrea; Busetto, Martina; Marcon, Francesca

SUPG-stabilized stabilization-free VEM: a numerical investigation. (English) Zbl 07889305

Math. Eng. (Springfield) 6, No. 1, Paper No. 8, 191 p. (2024).
Summary: We numerically investigate the possibility of defining Stabilization-Free Virtual Element discretizations-i.e., Virtual Element Method discretizations without an additional non-polynomial non-operator-preserving stabilization term-of advection-diffusion problems in the advection-dominated regime, considering a Streamline Upwind Petrov-Galerkin stabilized formulation of the scheme. We present numerical tests that assess the robustness of the proposed scheme and compare it with a standard Virtual Element Method.

Cited in 1 Document

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35B65 Smoothness and regularity of solutions to PDEs
35B35 Stability in context of PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness

Keywords:

virtual element methods; stabilization; streamline upwind Petrov-Galerkin; advection-diffusion; numerical tests

Software:

PolyMesher
Cite Review PDF
Full Text: DOI arXiv

References:

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