Anisotropic a posteriori error estimate for the virtual element method

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 e...

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Bibliographic Details
Published in:IMA journal of numerical analysis 2022-04, Vol.42 (2), p.1273-1312
Main Authors: Antonietti, P F, Berrone, S, Borio, A, D’Auria, A, Verani, M, Weisser, S
Format: Article
Language:English
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Summary: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.
ISSN:0272-4979
1464-3642
DOI:10.1093/imanum/drab001