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Superconvergence of a Galerkin FEM for Higher-Order Elements in Convection-Diffusion Problems

Published online by Cambridge University Press:  28 May 2015

Sebastian Franz  and
H.-G. Roos
Sebastian Franz*
Affiliation:
Institut für Numerische Mathematik, Technische Universität Dresden, 01062 Dresden, Germany
H.-G. Roos*
Affiliation:
Institut für Numerische Mathematik, Technische Universität Dresden, 01062 Dresden, Germany
*
Corresponding author.Email address:[email protected]
Corresponding author.Email address:[email protected]
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Abstract

In this paper we present a first supercloseness analysis for higher-order Galerkin FEM applied to a singularly perturbed convection-diffusion problem. Using a solution decomposition and a special representation of our finite element space, we are able to prove a supercloseness property of p + 1/4 in the energy norm where the polynomial order p ≥ 3 is odd.

Keywords

65N1265N3065N50Singular perturbationlayer-adapted meshessuperconvergencepostprocessing
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 7 , Issue 3 , August 2014 , pp. 356 - 373
Copyright
Copyright © Global Science Press Limited 2014

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