Agouzal, Abdellatif; Lipnikov, Konstantin; Vassilevski, Yuri Generation of quasi-optimal meshes based on a posteriori error estimates. (English) Zbl 1134.65310 Brewer, Michael L. (ed.) et al., Proceedings of the 16th international meshing roundtable, Seattle, WA, USA, October 14–17, 2007. Berlin: Springer (ISBN 978-3-540-75102-1/hbk). 139-158 (2008). We study methods for recovering tensor metrics from given error estimates and properties of meshes which are quasi-uniforrn 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.For the entire collection see [Zbl 1122.65002]. Cited in 1 Document MSC: 65D18 Numerical aspects of computer graphics, image analysis, and computational geometry 68U05 Computer graphics; computational geometry (digital and algorithmic aspects) Keywords:mesh optimization; recovering tensor metrics; error estimates; numerical experiments PDFBibTeX XMLCite \textit{A. Agouzal} et al., in: Proceedings of the 16th international meshing roundtable, Seattle, WA, USA, October 14--17, 2007. Berlin: Springer. 139--158 (2008; Zbl 1134.65310)