In the present paper we initiate the study of hp Virtual Elements. We focus on the case with uniform polynomial degree across the mesh and derive theoretical convergence estimates that are explicit both in the mesh size h and in the polynomial degree p in the case of finite Sobolev regularity. Exponential convergence is proved in the case of analytic solutions. The theoretical convergence results are validated in numerical experiments. Finally, an initial study on the possible choice of local basis functions is included.

Beirão Da Veiga, L., Chernov, A., Mascotto, L., & Russo, A. (2016). Basic principles of hp virtual elements on quasiuniform meshes. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 26(8), 1567-1598 [10.1142/S021820251650038X].

Basic principles of hp virtual elements on quasiuniform meshes

BEIRAO DA VEIGA, LOURENCO
Primo
;
MASCOTTO, LORENZO
Penultimo
;
RUSSO, ALESSANDRO
Ultimo
2016

Abstract

In the present paper we initiate the study of hp Virtual Elements. We focus on the case with uniform polynomial degree across the mesh and derive theoretical convergence estimates that are explicit both in the mesh size h and in the polynomial degree p in the case of finite Sobolev regularity. Exponential convergence is proved in the case of analytic solutions. The theoretical convergence results are validated in numerical experiments. Finally, an initial study on the possible choice of local basis functions is included.
Articolo in rivista - Articolo scientifico
hp error bounds; polygonal methods; Virtual elements;
hp error bounds; polygonal methods; Virtual elements; Applied Mathematics; Modeling and Simulation
English
1567
1598
32
Beirão Da Veiga, L., Chernov, A., Mascotto, L., & Russo, A. (2016). Basic principles of hp virtual elements on quasiuniform meshes. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 26(8), 1567-1598 [10.1142/S021820251650038X].
BEIRAO DA VEIGA, L; Chernov, A; Mascotto, L; Russo, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/131756
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