Geodesic
Quasi-Optimal Triangulations for Gradient Nonconforming Interpolates of Piecewise Regular Functions
A. Agouzal1 ; N. Debit1
1 University Lyon1, Institute Camille Jordan, UMR 5208, 69100 Villeurbanne, France
Mathematical modelling of natural phenomena, Tome 5 (2010) no. 7 Supplement, pp. 78-83

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Anisotropic adaptive methods based on a metric related to the Hessian of the solution are considered. We propose a metric targeted to the minimization of interpolation error gradient for a nonconforming linear finite element approximation of a given piecewise regular function on a polyhedral domain Ω of ℝd, d ≥ 2. We also present an algorithm generating a sequence of asymptotically quasi-optimal meshes relative to such a nonconforming discretization and give numerical asymptotic behavior of the error reduction produced by the generated mesh
DOI : 10.1051/mmnp/20105713

A. Agouzal 1 ; N. Debit 1

1 University Lyon1, Institute Camille Jordan, UMR 5208, 69100 Villeurbanne, France 
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A. Agouzal; N. Debit. Quasi-Optimal Triangulations for Gradient Nonconforming Interpolates of Piecewise Regular Functions. Mathematical modelling of natural phenomena, Tome 5 (2010) no. 7 Supplement, pp. 78-83. doi: 10.1051/mmnp/20105713

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

[2] E. D’Azevedo Optimal triangular mesh generation by coordinate transformation SIAM J. Sci. Comput. 1991 755 786

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

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