Volume 58, pp. 1-21, 2023.

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

Benjamin Dörich, Jan Leibold, and Bernhard Maier

Abstract

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

Full Text (PDF) [351 KB], BibTeX , DOI: 10.1553/etna_vol58s1

Key words

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

AMS subject classifications

65M12, 65N15, 65N30