Superconvergence of Discontinuous Finite Element Solutions for Transient Convection--diffusion Problems

Authors:
Slimane Adjerid;Andreas Klauser
Affiliations:
Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, USA 24061;Technical University of Munich, Garching, Munich, Germany 85748
Venue:
Journal of Scientific Computing
Year:
2005

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Foreword

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Foreword

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Abstract

We present a study of the local discontinuous Galerkin method for transient convection--diffusion problems in one dimension. We show that p-degree piecewise polynomial discontinuous finite element solutions of convection-dominated problems are O(驴x p+2) superconvergent at Radau points. For diffusion- dominated problems, the solution's derivative is O(驴x p+2) superconvergent at the roots of the derivative of Radau polynomial of degree p+1. Using these results, we construct several asymptotically exact a posteriori finite element error estimates. Computational results reveal that the error estimates are asymptotically exact.