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

Abstract

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