Anisotropic a posteriori error estimate for the virtual element method

被引：10
|
作者：
Antonietti, P. F. [1 ]
Berrone, S. [2 ]
Borio, A. [2 ]
D'Auria, A. [2 ]
Verani, M. [1 ]
Weisser, S. [3 ]
机构：
[1] Politecn Milan, Dipartimento Matemat, MOX, I-20133 Milan, Italy
[2] Politecn Torino, Dipartimento Sci Matemat, I-10129 Turin, Italy
[3] Univ Saarland, FR Math, Postfach 15 11 50, D-66041 Saarbrucken, Germany
来源：
IMA JOURNAL OF NUMERICAL ANALYSIS | 2022年 / 42卷 / 02期
关键词：
virtual element method; anisotropy; a posteriori error analysis; SUPERCONVERGENT PATCH RECOVERY; GRADIENT RECOVERY; MESHES; DISCRETIZATION;
D O I：
10.1093/imanum/drab001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：1273 / 1312
页数：40
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