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

Mark Ainsworth, Xinhui Ma

Research output: Contribution to journalArticle

12 Citations (Scopus)

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.
LanguageEnglish
Pages436-453
Number of pages18
JournalJournal of Computational Physics
Volume231
Issue number2
DOIs
Publication statusPublished - 20 Jan 2012

Fingerprint

Finite element method
Processing
approximation
electric motors
Electric motors
estimators
Poles
Materials properties
discontinuity
poles
derivation
Fluxes

Keywords

  • mixed finite element method
  • posteriori error estimation
  • post-processing
  • estimators
  • finite element methods
  • computable error bounds
  • flow in porous media
  • electromagnetics
  • equations

Cite this

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Non-uniform order mixed FEM approximation : implementation, post-processing, computable error bound and adaptivity. / Ainsworth, Mark; Ma, Xinhui.

In: Journal of Computational Physics, Vol. 231, No. 2, 20.01.2012, p. 436-453.

Research output: Contribution to journalArticle

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