In the present work, we analyze the hp version of virtual element methods for the 2D Poisson problem. We prove exponential convergence of the energy error employing sequences of polygonal meshes geometrically refined, thus extending the classical choices for the decomposition in the hp finite element framework to very general decomposition of the domain. A new stabilization for the discrete bilinear form with explicit bounds in h and p is introduced. Numerical experiments validate the theoretical results. We also exhibit a numerical comparison between hp virtual elements and hp finite elements.

Beirao da Veiga, L., Chernov, A., Mascotto, L., Russo, A. (2018). Exponential convergence of the hp virtual element method in presence of corner singularities. NUMERISCHE MATHEMATIK, 138(3), 581-613 [10.1007/s00211-017-0921-7].

Exponential convergence of the hp virtual element method in presence of corner singularities

Beirao da Veiga, L.;Mascotto, L.;Russo, A.
2018

Abstract

In the present work, we analyze the hp version of virtual element methods for the 2D Poisson problem. We prove exponential convergence of the energy error employing sequences of polygonal meshes geometrically refined, thus extending the classical choices for the decomposition in the hp finite element framework to very general decomposition of the domain. A new stabilization for the discrete bilinear form with explicit bounds in h and p is introduced. Numerical experiments validate the theoretical results. We also exhibit a numerical comparison between hp virtual elements and hp finite elements.
Articolo in rivista - Articolo scientifico
65N12; 65N15; 65N30; 65N50;
Computational Mathematics; Applied Mathematics
English
25-ott-2017
2018
138
3
581
613
open
Beirao da Veiga, L., Chernov, A., Mascotto, L., Russo, A. (2018). Exponential convergence of the hp virtual element method in presence of corner singularities. NUMERISCHE MATHEMATIK, 138(3), 581-613 [10.1007/s00211-017-0921-7].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/178200
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