Optimal $W^{1,\infty}$-estimates for an isoparametric finite element discretization of elliptic boundary value problems

Electronic Transactions on Numerical Analysis

article

Benjamin Dörich¹  Jan Leibold¹  Bernhard Maier¹ 

[1] Institute for Applied and Numerical Mathematics, Karlsruhe Institute of Technology

关键词: elliptic boundary value problem;    nonconforming space discretization;    isoparametric finite elements;    Ritz map;    maximum norm error estimates;    a priori error estimates;    weighted norms;   

DOI  :  10.1553/etna_vol58s1

学科分类：数学（综合）

来源: Kent State University * Institute of Computational Mathematics

【 摘 要 】

We consider an elliptic boundary value problem on a domain with regular boundary and discretize it with isoparametric finite elements of order $k\geq1$. We show optimal order of convergence of the isoparametric finite element solution in the $W^{1,\infty}$-norm. As an intermediate step, we derive stability and convergence estimates of optimal order $k$ for a (generalized) Ritz map.

【 授权许可】

Unknown