Anisotropic a posteriori error estimate for the Virtual Element Method
Keywords
Advanced Numerical Methods for Scientific Computing
Code:
56/2019
Title:
Anisotropic a posteriori error estimate for the Virtual Element Method
Date:
Monday 30th December 2019
Author(s):
Antonietti, P.F.; Berrone, S.; Borio A.; D'Auria A.; Verani, M.; Weisser, S.
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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.