Edge-based a Posteriori Error Estimators for Generating Quasi-optimal Simplicial Meshes

A. Agouzal; K. Lipnikov; Yu. Vassilevsk

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 5, Issue: 7, page 91-96
  • ISSN: 0973-5348

Abstract

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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

How to cite

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Agouzal, A., Lipnikov, K., and Vassilevsk, Yu.. Taik, A., ed. "Edge-based a Posteriori Error Estimators for Generating Quasi-optimal Simplicial Meshes." Mathematical Modelling of Natural Phenomena 5.7 (2010): 91-96. <http://eudml.org/doc/197673>.

@article{Agouzal2010,
abstract = {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},
author = {Agouzal, A., Lipnikov, K., Vassilevsk, Yu.},
editor = {Taik, A.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {finite elements; anisotropic meshes; a posteriori error estimates},
language = {eng},
month = {8},
number = {7},
pages = {91-96},
publisher = {EDP Sciences},
title = {Edge-based a Posteriori Error Estimators for Generating Quasi-optimal Simplicial Meshes},
url = {http://eudml.org/doc/197673},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Agouzal, A.
AU - Lipnikov, K.
AU - Vassilevsk, Yu.
AU - Taik, A.
TI - Edge-based a Posteriori Error Estimators for Generating Quasi-optimal Simplicial Meshes
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/8//
PB - EDP Sciences
VL - 5
IS - 7
SP - 91
EP - 96
AB - 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
LA - eng
KW - finite elements; anisotropic meshes; a posteriori error estimates
UR - http://eudml.org/doc/197673
ER -

References

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  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., 39 (1999), 1532–1551. 
  4. Y. Vassilevski, A. Agouzal. An unified asymptotic analysis of interpolation errors for optimal meshes. Doklady Mathematics, 72 (2005), 879–882. 

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