Optimal $W^{1,\infty}$-estimates for an isoparametric finite element discretization of elliptic boundary value problems
Benjamin Dörich, Jan Leibold, Bernhard Maier · ETNA - Electronic Transactions on Numerical Analysis · 2022
We consider an elliptic boundary value problem on a domain with regularboundary and discretize it with isoparametric finite elements of order$k\geq1$.We show optimal order of convergence of the isoparametric finiteelement solution in the $W^{1,\infty}$-norm. As an intermediate step,we derive stability and convergence estimates of optimal order $k$ fora (generalized) Ritz map.