Geodesic
Edge-based a Posteriori Error Estimators for Generating Quasi-optimal Simplicial Meshes
A. Agouzal1 ; K. Lipnikov2 ; Yu. Vassilevsk3
1 University Lyon1, Institute Camille Jordan, UMR 5208, 69100 Villeurbanne, France
2 Los Alamos National Laboratory, Los Alamos, NM, 87545, U.S.A.
3 Institute of Numerical Mathematics, Gubkina str. 8, Moscow 119333, Russia
Mathematical modelling of natural phenomena, Tome 5 (2010) no. 7 Supplement, pp. 91-96.

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We present a new method for generating a d-dimensional simplicial mesh that minimizes the Lp-norm, p > 0, of the interpolation error or its gradient. The method uses edge-based error estimates to build a tensor metric. We describe and analyze the basic steps of our method
DOI : 10.1051/mmnp/20105715

A. Agouzal 1 ; K. Lipnikov 2 ; Yu. Vassilevsk 3

1 University Lyon1, Institute Camille Jordan, UMR 5208, 69100 Villeurbanne, France
2 Los Alamos National Laboratory, Los Alamos, NM, 87545, U.S.A.
3 Institute of Numerical Mathematics, Gubkina str. 8, Moscow 119333, Russia 
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A. Agouzal; K. Lipnikov; Yu. Vassilevsk. Edge-based a Posteriori Error Estimators for Generating Quasi-optimal Simplicial Meshes. Mathematical modelling of natural phenomena, Tome 5 (2010) no. 7 Supplement, pp. 91-96. doi : 10.1051/mmnp/20105715. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20105715/

[1] A. Agouzal, K. Lipnikov, Y. Vassilevski. Generation of quasi-optimal meshes based on a posteriori error estimates. In: Proceedings of 16th International Meshing Roundtable. M.Brewer and D.Marcum (eds.), Springer, (2007), 139–148.

[2] A. Agouzal, K. Lipnikov, Y. Vassilevski. Hessian-free metric-based mesh adaptation via geometry of interpolation error. To appear in Comp. Math. Math. Phys., 50 (2010).

[3] Y. Vassilevski, K. Lipnikov Adaptive algorithm for generation of quasi-optimal meshes Comp. Math. Math. Phys. 1999 1532 1551

[4] Y. Vassilevski, A. Agouzal An unified asymptotic analysis of interpolation errors for optimal meshes Doklady Mathematics 2005 879 882

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