On an Adaptive LDG for the $P$-Laplace Problem

Abstract

In this paper we consider the adaptive local discontinuous Galerkin(LDG) method for the $p$-Laplace problem in polygonal regions in $\mathbb{R}^2$. We present new sharper a posteriori error estimate for the LDG approximation of the $p$-Laplacian in the new framework. Several examples are given to confirm the reliability of the estimate.