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A New Anisotropic Mesh Adaptation MethodBased upon Hierarchical A Posteriori ErrorEstimates

Kamenski, Lennard, Weizhang Huang, and Jens Lang

Reserach Notes, 18th International Meshing Roundtable, Springer-Verlag, pp.11-15, October 25-28 2009

IMR
PROCEEDINGS

18th International Meshing Roundtable
Salt Lake City, UT, USA.
October 25-28, 2009

Technische UniversitĀ®at Darmstadt kamenski@mathematik.tu-darmstadt.de
University of Kansas, Lawrence huang@math.ku.edu
Technische UniversitĀ®at Darmstadt lang@mathematik.tu-darmstadt.de

Abstract
An anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is considered. The adaptation method generates anisotropic adaptive meshes as quasi-uniform ones in some metric space. The as- sociated metric tensor is computed by means of a posteriori hierarchical error es- timates. A global hierarchical error estimate is employed in this study to obtain reliable directional information of the solution. Mesh examples are presented for the mathematical model for heat conduction in a thermal battery with large orthotropic jumps in the material coefficients4.

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