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Multi-Dimensional Continuous Metric for Mesh Adaptation

Alauzet, Frederic, Adrien Loseille, Alain Dervieux, and Pascal Frey

Proceedings, 15th International Meshing Roundtable, Springer-Verlag, pp.191-214, September 17-20 2006

IMR
PROCEEDINGS

15th International Meshing Roundtable
Birmingham, Alabama, U.S.A.
September 17-20, 2006

Frederic Alauzet, Adrien Loseille
INRIA-Gamma, Domaine de Voluceau, BP 105, 78153 Le Chesnay cedex, France
Frederic.Alauzet@inria.fr and Adrien.Loseille@inria.fr

Alain Dervieux
INRIA-Tropics, BP 93, 06902 Sophia-Antipolis, France
Alain.Dervieux@inria.fr

Pascal Frey
UMPC/Lab. J-L Lions, BP 187, 75252 Paris Cedex 05, France
frey@ann.jussieu.fr

Abstract
Mesh adaptation is considered here as the research of an optimum that minimizes the P1 interpolation error of a function u of Rn given a number of vertices. A continuous modeling is described by considering classes of equivalence between meshes which are analytically represented by a metric tensor field. Continuous metrics are exhibited for Lp error model and mesh order of convergence are analyzed. Numerical examples are provided in two and three dimensions.

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