An hp-Analysis of the Local Discontinuous Galerkin Method for Diffusion Problems

Authors:
Ilaria Perugia;Dominik Schötzau
Affiliations:
Department of Mathematics, University of Pavia, Via Ferrata 1, 27100, Pavia, Italy. perugia@dimat.unipv.it;Department of Mathematics, University of Basel, Rheinsprung 21, 4051 Basel, Switzerland. schotzau@math.unibas.ch
Venue:
Journal of Scientific Computing
Year:
2002

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Abstract

We present an hp-error analysis of the local discontinuous Galerkin method for diffusion problems, considering unstructured meshes with hanging nodes and two- and three-dimensional domains. Our estimates are optimal in the meshsize h and slightly suboptimal in the polynomial approximation order p. Optimality in p is achieved for matching grids and polynomial boundary conditions.