Mortar spectral method in axisymmetric domains

Saloua Mani Aouadi; Jamil Satouri

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

  • Volume: 47, Issue: 1, page 33-55
  • ISSN: 0764-583X

Abstract

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We consider the Laplace equation posed in a three-dimensional axisymmetric domain. We reduce the original problem by a Fourier expansion in the angular variable to a countable family of two-dimensional problems. We decompose the meridian domain, assumed polygonal, in a finite number of rectangles and we discretize by a spectral method. Then we describe the main features of the mortar method and use the algorithm Strang Fix to improve the accuracy of our discretization.

How to cite

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Mani Aouadi, Saloua, and Satouri, Jamil. "Mortar spectral method in axisymmetric domains." ESAIM: Mathematical Modelling and Numerical Analysis 47.1 (2012): 33-55. <http://eudml.org/doc/222134>.

@article{ManiAouadi2012,
abstract = {We consider the Laplace equation posed in a three-dimensional axisymmetric domain. We reduce the original problem by a Fourier expansion in the angular variable to a countable family of two-dimensional problems. We decompose the meridian domain, assumed polygonal, in a finite number of rectangles and we discretize by a spectral method. Then we describe the main features of the mortar method and use the algorithm Strang Fix to improve the accuracy of our discretization.},
author = {Mani Aouadi, Saloua, Satouri, Jamil},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Axisymmetric domains; mortar method; spectral methods; Laplace equation; axisymmetric domains; Fourier expansion; a priori error estimates; numerical experiments; convergence},
language = {eng},
month = {7},
number = {1},
pages = {33-55},
publisher = {EDP Sciences},
title = {Mortar spectral method in axisymmetric domains},
url = {http://eudml.org/doc/222134},
volume = {47},
year = {2012},
}

TY - JOUR
AU - Mani Aouadi, Saloua
AU - Satouri, Jamil
TI - Mortar spectral method in axisymmetric domains
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2012/7//
PB - EDP Sciences
VL - 47
IS - 1
SP - 33
EP - 55
AB - We consider the Laplace equation posed in a three-dimensional axisymmetric domain. We reduce the original problem by a Fourier expansion in the angular variable to a countable family of two-dimensional problems. We decompose the meridian domain, assumed polygonal, in a finite number of rectangles and we discretize by a spectral method. Then we describe the main features of the mortar method and use the algorithm Strang Fix to improve the accuracy of our discretization.
LA - eng
KW - Axisymmetric domains; mortar method; spectral methods; Laplace equation; axisymmetric domains; Fourier expansion; a priori error estimates; numerical experiments; convergence
UR - http://eudml.org/doc/222134
ER -

References

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  14. R. Pasquetti, L.F. Pavarino, F. Rapetti and E. Zampieri, Overlapping Schwarz methods for Fekete and Gauss–Lobatto spectral elements. SIAM J. Scient. Comput.29 (2007) 1073–1092.  Zbl1141.65394
  15. Y. Maday, C. Mavriplis and A.T. Patera, Nonconforming mortar element methods : application to spectral discretizations, in Domain decomposition methods. SIAM (1989) 392–418.  Zbl0692.65055
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