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

Mathematical Modelling of Natural Phenomena (2010)

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

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topAgouzal, 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

top- 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. Zbl1134.65310
- E. D’Azevedo. Optimal triangular mesh generation by coordinate transformation. SIAM J. Sci. Comput., 12 (1991), 755–786. Zbl0736.65001
- Y. Vassilevski, K. Lipnikov. Adaptive algorithm for generation of quasi-optimal meshes. Comp. Math. Math. Phys., 39 (1999), 1532–1551.

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