Families of Meshes Minimizing P 1 Interpolation Error [chapter]

A. Agouzal, K. Lipnikov, Y. Vassilevski
2011 Proceedings of the 20th International Meshing Roundtable  
For a given function, we consider a problem of minimizing the P 1 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
more » ... ed with numerical examples.
doi:10.1007/978-3-642-24734-7_17 dblp:conf/imr/AgouzalLV11 fatcat:hjv6zldkhfcwhigwkrgtfosc54