%0 Journal Article
%T $L^{\infty}$-error estimate for the finite element method on two dimensional surfaces
%A Heiko Kr£¿ner
%J Mathematics
%D 2015
%I arXiv
%X We approximate the solution of the equation $$ -\Delta_S u+u = f $$ on a two-dimensional, embedded, orientable, closed surface $S$ where $-\Delta_S$ denotes the Laplace Beltrami operator on $S$ by using continuous, piecewise linear finite elements on a triangulation of $S$ with flat triangles. We show that the $L^{\infty}$-error is of order $O(h^2|\log h|)$ as in the corresponding situation in an Euclidean setting.
%U http://arxiv.org/abs/1508.06035v2