The virtual element method was introduced 10 years ago, and has generated a large number of theoretical results and applications ever since. Here, we overview the main mathematical results concerning the stabilization of the method as an introduction for newcomers in the field. In particular, we summarize the proofs of some results for two dimensional “nodal” conforming and nonconforming virtual element spaces to pinpoint the essential tools used in the stability analysis. We discuss their extensions to several other virtual elements. Finally, we show several ways to prove the interpolation estimates, including a recent one that is based on employing the stability bounds.

Mascotto, L. (2023). The role of stabilization in the virtual element method: A survey. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 151(1 December 2023), 244-251 [10.1016/j.camwa.2023.09.045].

The role of stabilization in the virtual element method: A survey

Mascotto, L
2023

Abstract

The virtual element method was introduced 10 years ago, and has generated a large number of theoretical results and applications ever since. Here, we overview the main mathematical results concerning the stabilization of the method as an introduction for newcomers in the field. In particular, we summarize the proofs of some results for two dimensional “nodal” conforming and nonconforming virtual element spaces to pinpoint the essential tools used in the stability analysis. We discuss their extensions to several other virtual elements. Finally, we show several ways to prove the interpolation estimates, including a recent one that is based on employing the stability bounds.
Articolo in rivista - Articolo scientifico
Interpolation estimate; Stability bound; Virtual element method;
English
11-ott-2023
2023
151
1 December 2023
244
251
none
Mascotto, L. (2023). The role of stabilization in the virtual element method: A survey. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 151(1 December 2023), 244-251 [10.1016/j.camwa.2023.09.045].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/442638
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