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

[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.

[学科分类] 数学（综合）

[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