Generation of quasi-optimal meshes based on a posteriori error estimates

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Abstract

We study methods for recovering tensor metrics from given error estimates and properties of meshes which are quasi-uniform in these metrics. We derive optimal upper and lower bounds for the global error on these meshes. We demonstrate with numerical experiments that the edge-based error estimates are preferable for recovering anisotropic metrics than the conventional element-based errors estimates.

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Agouzal, A., Lipnikov, K., & Vassilevski, Y. (2008). Generation of quasi-optimal meshes based on a posteriori error estimates. In Proceedings of the 16th International Meshing Roundtable, IMR 2007 (pp. 139–148). https://doi.org/10.1007/978-3-540-75103-8_8

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