SUPG-stabilized stabilization-free VEM: a numerical investigation

Andrea Borio; Martina Busetto; Francesca Marcon; Andrea Borio; Martina Busetto; Francesca Marcon

doi:10.3934/mine.2024008

Mathematics in Engineering

2024, Volume 6, Issue 1: 173-191. doi: 10.3934/mine.2024008

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SUPG-stabilized stabilization-free VEM: a numerical investigation

1.
Dipartimento di Scienze Matematiche, Politecnico di Torino, Torino 10129, Italy
2.
ABB Switzerland, Corporate Research, 5405 Baden-Dättwil, Switzerland

Received: 29 June 2023 Revised: 27 February 2024 Accepted: 27 February 2024 Published: 01 March 2024

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.
- Virtual Element Methods,
- stabilization,
- Streamline Upwind Petrov-Galerkin,
- advection-diffusion,
- numerical tests
Citation: Andrea Borio, Martina Busetto, Francesca Marcon. SUPG-stabilized stabilization-free VEM: a numerical investigation[J]. Mathematics in Engineering, 2024, 6(1): 173-191. doi: 10.3934/mine.2024008

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Abstract

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.

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