Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-22T21:10:15.522Z Has data issue: false hasContentIssue false
  • English
  • Français

Mortar spectral method in axisymmetric domains

Published online by Cambridge University Press:  31 July 2012

Saloua Mani Aouadi  and
Jamil Satouri
Saloua Mani Aouadi
Affiliation:
Faculty of Sciences of Tunis, University Tunis El Manar, 2090 Tunis, Tunisia. [email protected]
Jamil Satouri
Affiliation:
Faculty of Sciences of Tunis, University Tunis El Manar, 2090 Tunis, Tunisia. [email protected]
Get access

Abstract

We consider the Laplace equation posed in a three-dimensional axisymmetric domain. Wereduce the original problem by a Fourier expansion in the angular variable to a countablefamily 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 describethe main features of the mortar method and use the algorithm Strang Fix to improve theaccuracy of our discretization.

Keywords

Axisymmetric domainsmortar methodspectral methodsLaplace equation
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 1 , January 2013 , pp. 33 - 55
Copyright
© EDP Sciences, SMAI, 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abdallah, A.B., Belgacem, F.B., Maday, Y. and Rapetti, F., Mortaring the two-dimensional edge finite elements for the discretization of some electromagnetic models. Math. Mod. Methods Appl. Sci. 14 (2004) 1635–1656. Google Scholar
M. Azaïez, C. Bernardi, M. Dauge and Y. Maday, Spectral Methods for Axisymetric Domains. Series in Appl. Math. 3 (1999).
Belgacem, F.B., Bernardi, C. and Rapetti, F., Numerical analysis of a model for an axisymmetric guide for electromagnetic waves. Part I : The continuous problem and its Fourier expansion. Math. Meth. Appl. Sci. 28 (2005) 2007–2029. Google Scholar
Bernardi, C. and Maday, Y., Properties of some weighted Sobolev spaces and application to spectral approximations. SIAM J. Numer. Anal. 26 (1989) 769–829. Google Scholar
C. Bernardi and Y. Maday, Approximations spectrales de problèmes aux limites elliptiques. Math. Appl. 10 (1992).
C. Bernardi, M. Dauge and M. Azaïez, Numerical Analysis and Spectral Methods in Axisymetric Problems. Rapport Interne, Laboratoire d’Analyse Numérique, Université Pierre et Marie Curie (1995).
Bertoluzza, S., Perrier, S. Falletta and V., The Mortar method in the wavelet context. Model. Math. Anal. Numer. 35 (2001) 647–673. Google Scholar
H. Brezis, Analyse fonctionnelle, in Théorie et Applications. Masson, Paris (1983).
N. Chorfi, Traitement de singularités géométriques par méthode d’éléments spectraux avec joints. Thèse de l’Université Pierre et Marie Curie, Paris VI (1998).
M. Dauge, Elliptic Boundary Value Problems on Corner Domains. Lect. Notes Math. 1341 (1988).
V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations, in Theory and Algorithms. Springer-Verlag (1986).
P. Grisvard, Singularities in boundary value problems, in Collect. RMA 22 (1992).
P. Le Tallec, Domain decomposition methods in computational mechanics, in Comput. Mech. Adv. North-Holland (1994).
Pasquetti, R., Pavarino, L.F., Rapetti, F. and Zampieri, E., Overlapping Schwarz methods for Fekete and Gauss–Lobatto spectral elements. SIAM J. Scient. Comput. 29 (2007) 1073–1092. Google Scholar
Y. Maday, C. Mavriplis and A.T. Patera, Nonconforming mortar element methods : application to spectral discretizations, in Domain decomposition methods. SIAM (1989) 392–418.
J. Satouri, Méthodes d’éléments spectraux avec joints pour des géométries axisymétriques. Thèse de l’Université Pierre et Marie Curie, Paris VI (2010).
G. Strang and G.J. Fix, An Analysis of the Finite Element Method, in Automatic Computation. Prentice Hall Serie (1973).