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Higher-Order Interpolation for Mesh Adaptation

Mbinky, Estelle, Frederic Alauzet and Adrien Loseille

Research Notes, 21st International Meshing Roundtable, Springer-Verlag, pp.Research Note, October 7-10 2012


21st International Meshing Roundtable
San Jose, CA
October 7-10, 2012

INRIA, Gamma Project, Rocquencourt, BP 105, 78153 Le Chesnay Cedex, France
Email: {Estelle.Mbinky,Frederic.Alauzet,Adrien.Loseille}

This paper addresses the construction of anisotropic metrics from higher-order interpolation error in 2 dimensions [2, 3] for mesh adaptation. Our approach is based on homogeneous polynomials that model a local interpolation error. Optimal orientation and ratios are found by using the Sylvester decomposition [4]. Then we apply a global calculus of variation to get the optimal metric field minimizing the Lp norm of the interpolation error. We illustrate this approach on a numerical example.

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