We construct a nonconforming virtual element method (ncVEM) based on approximation spaces that are enriched with special singular functions. This enriched ncVEM is tailored for the approximation of solutions to elliptic problems, which have singularities due to the geometry of the domain. Differently from the traditional extended Galerkin method approach, based on the enrichment of local spaces with singular functions, no partition of unity is employed. Rather, the design of the method hinges upon the special structure of the nonconforming virtual element spaces. We discuss the theoretical analysis of the method and support it with several numerical experiments. We also present an orthonormalization procedure that drastically trims the ill-conditioning of the final system.

Artioli, E., Mascotto, L. (2021). Enrichment of the nonconforming virtual element method with singular functions. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 385 [10.1016/j.cma.2021.114024].

Enrichment of the nonconforming virtual element method with singular functions

Artioli E.;
2021-01-01

Abstract

We construct a nonconforming virtual element method (ncVEM) based on approximation spaces that are enriched with special singular functions. This enriched ncVEM is tailored for the approximation of solutions to elliptic problems, which have singularities due to the geometry of the domain. Differently from the traditional extended Galerkin method approach, based on the enrichment of local spaces with singular functions, no partition of unity is employed. Rather, the design of the method hinges upon the special structure of the nonconforming virtual element spaces. We discuss the theoretical analysis of the method and support it with several numerical experiments. We also present an orthonormalization procedure that drastically trims the ill-conditioning of the final system.
2021
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore ICAR/08 - SCIENZA DELLE COSTRUZIONI
English
Enrichment
Extended Galerkin method
Optimal convergence
Polygonal mesh
Singular function
Virtual element method
Artioli, E., Mascotto, L. (2021). Enrichment of the nonconforming virtual element method with singular functions. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 385 [10.1016/j.cma.2021.114024].
Artioli, E; Mascotto, L
Articolo su rivista
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/313560
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