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

A. Agouzal; N. Debit

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 5, Issue: 7, page 78-83
  • ISSN: 0973-5348

Abstract

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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

How to cite

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Agouzal, A., and Debit, N.. Taik, A., ed. "Quasi-Optimal Triangulations for Gradient Nonconforming Interpolates of Piecewise Regular Functions." Mathematical Modelling of Natural Phenomena 5.7 (2010): 78-83. <http://eudml.org/doc/197626>.

@article{Agouzal2010,
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},
author = {Agouzal, A., Debit, N.},
editor = {Taik, A.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {finite elements; anisotropic meshes},
language = {eng},
month = {8},
number = {7},
pages = {78-83},
publisher = {EDP Sciences},
title = {Quasi-Optimal Triangulations for Gradient Nonconforming Interpolates of Piecewise Regular Functions},
url = {http://eudml.org/doc/197626},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Agouzal, A.
AU - Debit, N.
AU - Taik, A.
TI - Quasi-Optimal Triangulations for Gradient Nonconforming Interpolates of Piecewise Regular Functions
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/8//
PB - EDP Sciences
VL - 5
IS - 7
SP - 78
EP - 83
AB - 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
LA - eng
KW - finite elements; anisotropic meshes
UR - http://eudml.org/doc/197626
ER -

References

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  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., 12 (1991), 755–786. 
  3. Y. Vassilevski, K. Lipnikov. Adaptive algorithm for generation of quasi-optimal meshes. Comp. Math. Math. Phys., 39 (1999), 1532–1551. 

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