A new methodology for anisotropic mesh refinement based upon error gradients

Authors:
Thomas Apel;Sergei Grosman;Peter K. Jimack;Arnd Meyer
Affiliations:
Fakultät für Mathematik, Technische Universität Chemnitz, 09107 Chemnitz, Germany;Fakultät für Mathematik, Technische Universität Chemnitz, 09107 Chemnitz, Germany;Computational PDE Unit, School of Computing, University of Leeds, Leeds LS2 9JT, UK;Fakultät für Mathematik, Technische Universität Chemnitz, 09107 Chemnitz, Germany
Venue:
Applied Numerical Mathematics
Year:
2004

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Abstract

We introduce a new strategy for controlling the use of anisotropic mesh refinement based upon the gradients of an a posteriori approximation of the error in a computed finite element solution. The efficiency of this strategy is demonstrated using a simple anisotropic mesh adaption algorithm and the quality of a number of potential a posteriori error estimates is considered.