Anisotropic a posteriori error estimate for the virtual element method. (22nd February 2021)

• Record Type: Journal Article
• Authors: Antonietti, P F; Berrone, S; Borio, A; D'Auria, A; Verani, M; Weisser, S
• Is Part Of: IMA journal of numerical analysis. Volume 42:Number 2(2022)
• Page Start: 1273
• Page End: 1312
• Publication Date: 2021-02-22
• Subjects: virtual element method -- anisotropy -- a posteriori error analysis; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/drab001
• Languages: English
• ISSNs: 0272-4979

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.