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Anisotropic Mesh Adaptation for Solution ofFinite Element Problems Using HierarchicalEdge-Based Error Estimates

Agouzal, Abdellatif, Konstantin Lipnikov, and Yuri Vassilevski

Proceedings, 18th International Meshing Roundtable, Springer-Verlag, pp.595-610, October 25-28 2009

IMR
PROCEEDINGS

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

Universite de Lyon 1, Laboratoire díAnalyse Numerique
agouzal@univ-lyon1.fr
Los Alamos National Laboratory, Theoretical Division
lipnikov@lanl.gov
Institute of Numerical Mathematics
yuri.vassilevski@gmail.com

Abstract
We present a new technology for generating meshes minimizing the interpolation and discretization errors or their gradients. The key element of this methodology is construction of a space metric from edge-based error estimates. For a mesh with Nh triangles, the error is proportional to N-1h and the gradient of error is proportional to Nh -1/2 which are the optimal asymptotics. The methodology is verified with numerical experiments.

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