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.
CITATION STYLE
Agouzal, A., Lipnikov, K., & Vassilevski, Y. (2011). Families of meshes minimizing P1 interpolation error. In Proceedings of the 20th International Meshing Roundtable, IMR 2011 (pp. 313–327). Kluwer Academic Publishers. https://doi.org/10.1007/978-3-642-24734-7_17
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