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.
Keywords: axisymmetric domains, mortar method, spectral methods, Laplace equation
@article{M2AN_2013__47_1_33_0, author = {Mani Aouadi, Saloua and Satouri, Jamil}, title = {Mortar spectral method in axisymmetric domains}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {33--55}, publisher = {EDP-Sciences}, volume = {47}, number = {1}, year = {2013}, doi = {10.1051/m2an/2012018}, mrnumber = {2968694}, zbl = {1277.65101}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2012018/} }
TY - JOUR AU - Mani Aouadi, Saloua AU - Satouri, Jamil TI - Mortar spectral method in axisymmetric domains JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2013 SP - 33 EP - 55 VL - 47 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2012018/ DO - 10.1051/m2an/2012018 LA - en ID - M2AN_2013__47_1_33_0 ER -
%0 Journal Article %A Mani Aouadi, Saloua %A Satouri, Jamil %T Mortar spectral method in axisymmetric domains %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2013 %P 33-55 %V 47 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2012018/ %R 10.1051/m2an/2012018 %G en %F M2AN_2013__47_1_33_0
Mani Aouadi, Saloua; Satouri, Jamil. Mortar spectral method in axisymmetric domains. ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 (2013) no. 1, pp. 33-55. doi : 10.1051/m2an/2012018. http://www.numdam.org/articles/10.1051/m2an/2012018/
[1] Mortaring the two-dimensional edge finite elements for the discretization of some electromagnetic models. Math. Mod. Methods Appl. Sci. 14 (2004) 1635-1656. | MR | Zbl
, , and ,[2] Spectral Methods for Axisymetric Domains. Series in Appl. Math. 3 (1999). | Zbl
, , and ,[3] 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. | MR | Zbl
, and ,[4] Properties of some weighted Sobolev spaces and application to spectral approximations. SIAM J. Numer. Anal. 26 (1989) 769-829. | MR | Zbl
and ,[5] Approximations spectrales de problèmes aux limites elliptiques. Math. Appl. 10 (1992). | Zbl
and ,[6] Numerical Analysis and Spectral Methods in Axisymetric Problems. Rapport Interne, Laboratoire d'Analyse Numérique, Université Pierre et Marie Curie (1995).
, and ,[7] The Mortar method in the wavelet context. Model. Math. Anal. Numer. 35 (2001) 647-673. | Numdam | MR | Zbl
, and ,[8] Analyse fonctionnelle, in Théorie et Applications. Masson, Paris (1983). | MR | Zbl
,[9] Traitement de singularités géométriques par méthode d'éléments spectraux avec joints. Thèse de l'Université Pierre et Marie Curie, Paris VI (1998).
,[10] Elliptic Boundary Value Problems on Corner Domains. Lect. Notes Math. 1341 (1988). | MR | Zbl
,[11] Finite Element Methods for Navier-Stokes Equations, in Theory and Algorithms. Springer-Verlag (1986). | MR | Zbl
and ,[12] Singularities in boundary value problems, in Collect. RMA 22 (1992). | MR | Zbl
,[13] Domain decomposition methods in computational mechanics, in Comput. Mech. Adv. North-Holland (1994). | MR | Zbl
,[14] Overlapping Schwarz methods for Fekete and Gauss-Lobatto spectral elements. SIAM J. Scient. Comput. 29 (2007) 1073-1092. | MR | Zbl
, , and ,[15] Nonconforming mortar element methods : application to spectral discretizations, in Domain decomposition methods. SIAM (1989) 392-418. | MR | Zbl
, and ,[16] Méthodes d'éléments spectraux avec joints pour des géométries axisymétriques. Thèse de l'Université Pierre et Marie Curie, Paris VI (2010).
,[17] An Analysis of the Finite Element Method, in Automatic Computation. Prentice Hall Serie (1973). | MR | Zbl
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