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

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

Year:    2014

Numerical Mathematics: Theory, Methods and Applications, Vol. 7 (2014), Iss. 3 : pp. 356–373

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.2014.1320nm

Numerical Mathematics: Theory, Methods and Applications, Vol. 7 (2014), Iss. 3 : pp. 356–373

Published online:    2014-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Singular perturbation layer-adapted meshes superconvergence postprocessing

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