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Families of Meshes Minimizing P1 Interpolation Error

Agouzal, A., K. Lipnikov and Y. Vassilevski

20th International Meshing Roundtable, Springer-Verlag, pp.313-326, October 23-26 2011

IMR
PROCEEDINGS

20th International Meshing Roundtable
Paris, France
October 23-26, 2011

I.C.J. Universite Lyon, France
Email:agouzal@univ-lyon1.fr

Summary
For a given function, we consider a problem of minimizing the P1 interpolation error on a set of triangulations with a fixed number of triangles. The minimization problem is reformulated as a problem of generating a mesh which is quasi-uniform in a specially designed metric. For functions with indefinite Hessian, we show existence of a family of metrics with highly diverse properties. The family may include both anisotropic and isotropic metrics. A developed theory is verified with numerical examples.

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