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Quasi-Optimal Triangulations for Gradient Nonconforming Interpolates of Piecewise Regular Functions

Published online by Cambridge University Press:  26 August 2010

A. Taik ,
A. Agouzal  and
N. Debit
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Abstract

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

Keywords

finite elementsanisotropic meshes
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 7: JANO9 – The 9th International Conference on Numerical Analysis and Optimization , 2010 , pp. 78 - 83
Copyright
© EDP Sciences, 2010

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References

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.
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Vassilevski, Y., Lipnikov, K.. Adaptive algorithm for generation of quasi-optimal meshes . Comp. Math. Math. Phys., 39 (1999), 1532–1551.Google Scholar