Linear Convergence of an Adaptive Finite Element Method for the p-Laplacian Equation

Abstract

We study an adaptive finite element method for the $p$-Laplacian like PDEs using piecewise linear, continuous functions. The error is measured by means of the quasi norm of Barrett and Liu. We provide residual based error estimators without a gap between the upper and lower bound. We show linear convergence of the algorithm which is similar to the one of Morin, Nochetto, and Siebert. All results are obtained without extra marking for the oscillation.