Summary
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 examples.
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Agouzal, A., Lipnikov, K., Vassilevski, Y. (2011). Families of Meshes Minimizing P 1 Interpolation Error. In: Quadros, W.R. (eds) Proceedings of the 20th International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24734-7_17
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DOI: https://doi.org/10.1007/978-3-642-24734-7_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24733-0
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