Repository: Freie Universität Berlin, Math Department

A new anisotropic mesh adaption method based upon hierarchical a posteriori error estimates

Huang, W. and Kamenski, L. and Lang, J. (2010) A new anisotropic mesh adaption method based upon hierarchical a posteriori error estimates. J. Comput. Phys., 229 . pp. 2179-2198.

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Abstract. A new anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in some metric space, with the metric tensor being computed based on hierarchical a posteriori error estimates. A global hierarchical error estimate is employed in this study to obtain reliable directional information of the solution. Instead of solving the global error problem exactly, which is costly in general, we solve it iteratively using the symmetric Gauß-Seidel method. Numerical results show that a few GS iterations are sufficient for obtaining a reasonably good approximation to the error for use in anisotropic mesh adaptation. The new method is compared with several strategies using local error estimators or recovered Hessians. Numerical results are presented for a selection of test examples and a mathematical model for heat conduction in a thermal battery with large orthotropic jumps in the material coefficients.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
ID Code:976
Deposited By: Ulrike Eickers
Deposited On:21 Oct 2010 14:06
Last Modified:21 Oct 2010 14:06

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