We introduce a nonconforming virtual element method for the Poisson problem on domains with fixed curved boundary and internal interfaces. We prove arbitrary order optimal convergence in the energy and L2 norms, and assess the theoretical results with numerical experiments. The proposed scheme has the upside that it can be designed and analyzed in any dimension.
Beirao da Veiga, L., Liu, Y., Mascotto, L., Russo, A. (2024). The nonconforming virtual element method with curved edges. JOURNAL OF SCIENTIFIC COMPUTING, 99(1 (April 2024)) [10.1007/s10915-023-02441-w].
The nonconforming virtual element method with curved edges
Beirao da Veiga, L.;Mascotto, L.;Russo, A.
2024
Abstract
We introduce a nonconforming virtual element method for the Poisson problem on domains with fixed curved boundary and internal interfaces. We prove arbitrary order optimal convergence in the energy and L2 norms, and assess the theoretical results with numerical experiments. The proposed scheme has the upside that it can be designed and analyzed in any dimension.
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