The Virtual Element Method (VEM) for diffusion-convection-reaction problems is considered. In order to design a quasi-robust scheme also in the convection-dominated regime, a Continuous Interior Penalty approach is employed. Due to the presence of polynomial projection operators, typical of the VEM, the stability and the error analysis requires particular care-especially in treating the advective term. Some numerical tests are presented to support the theoretical results.
Beirão Da Veiga, L., Lovadina, C., Trezzi, M. (2025). CIP-stabilized virtual elements for diffusion-convection-reaction problems. IMA JOURNAL OF NUMERICAL ANALYSIS, 45(2), 934-970 [10.1093/imanum/drae020].
CIP-stabilized virtual elements for diffusion-convection-reaction problems
Beirão Da Veiga L.;Trezzi M.
2025
Abstract
The Virtual Element Method (VEM) for diffusion-convection-reaction problems is considered. In order to design a quasi-robust scheme also in the convection-dominated regime, a Continuous Interior Penalty approach is employed. Due to the presence of polynomial projection operators, typical of the VEM, the stability and the error analysis requires particular care-especially in treating the advective term. Some numerical tests are presented to support the theoretical results.
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