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Non-uniform order mixed FEM approximation : implementation, post-processing, computable error bound and adaptivity

Ainsworth, Mark and Ma, Xinhui (2012) Non-uniform order mixed FEM approximation : implementation, post-processing, computable error bound and adaptivity. Journal of Computational Physics, 231 (2). pp. 436-453. ISSN 0021-9991

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Abstract

The present work provides a straightforward and focused set of tools and corresponding theoretical support for the implementation of an adaptive high order finite element code with guaranteed error control for the approximation of elliptic problems in mixed form. The work contains: details of the discretisation using non-uniform order mixed finite elements of arbitrarily high order; a new local post-processing scheme for the primary variable; the use of the post-processing scheme in the derivation of new, fully computable bounds for the error in the flux variable; and, an hp-adaptive refinement strategy based on the a posteriori error estimator. Numerical examples are presented illustrating the results obtained when the procedure is applied to a challenging problem involving a ten-pole electric motor with singularities arising from both geometric features and discontinuities in material properties. The procedure is shown to be capable of producing high accuracy numerical approximations with relatively modest numbers of unknowns.

Item type: Article
ID code: 40195
Keywords: mixed finite element method, posteriori error estimation, post-processing, estimators, finite element methods, computable error bounds, flow in porous media, electromagnetics, equations, Physics, Physics and Astronomy (miscellaneous), Computer Science Applications
Subjects: Science > Physics
Department: Faculty of Science > Mathematics and Statistics
Related URLs:
Depositing user: Pure Administrator
Date Deposited: 22 Jun 2012 15:34
Last modified: 27 Mar 2014 10:12
URI: http://strathprints.strath.ac.uk/id/eprint/40195

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