Anisotropic a posteriori error estimate for the virtual element method-Reference-Cited by-同舟云学术

Anisotropic a posteriori error estimate for the virtual element method

Published:2021-02-22 Issue: Volume: Page:
ISSN:0272-4979
Container-title:IMA Journal of Numerical Analysis
language:en
Short-container-title:

Author:

Antonietti P F¹,Berrone S²,Borio A²,D’Auria A²,Verani M¹,Weisser S³

Affiliation:

1. MOX, Dipartimento di Matematica, Politecnico di Milano, 20133, Italy

2. Dipartimento di Scienze Matematiche, Politecnico di Torino, 10129, Italy

3. FR Mathematik, Universität des Saarlandes, Postfach 15 11 50, D-66041 Saarbrücken, Germany

Abstract

Abstract We derive an anisotropic a posteriori error estimate for the adaptive conforming virtual element approximation of a paradigmatic two-dimensional elliptic problem. In particular, we introduce a quasi-interpolant operator and exploit its approximation results to prove the reliability of the error indicator. We design and implement the corresponding adaptive polygonal anisotropic algorithm. Several numerical tests assess the superiority of the proposed algorithm in comparison with standard polygonal isotropic mesh refinement schemes.

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics,Computational Mathematics,General Mathematics

Link

http://academic.oup.com/imajna/advance-article-pdf/doi/10.1093/imanum/drab001/36333366/drab001.pdf

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4. A residual based error estimator for the mimetic finite difference method;Beirão da Veiga;Numer. Math.,2008

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