This paper deals with the mortar spectral element discretization of two equivalent problems, the Laplace equation and the Darcy system, in a domain which corresponds to a nonhomogeneous anisotropic medium. The numerical analysis of the discretization leads to optimal error estimates and the numerical experiments that we present enable us to verify its efficiency.
Mots clés : Mortar method, spectral elements, Laplace equation, Darcy equation
@article{M2AN_2007__41_4_801_0, author = {Belhachmi, Zakaria and Bernardi, Christine and Karageorghis, Andreas}, title = {Mortar spectral element discretization of the {Laplace} and {Darcy} equations with discontinuous coefficients}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {801--824}, publisher = {EDP-Sciences}, volume = {41}, number = {4}, year = {2007}, doi = {10.1051/m2an:2007035}, mrnumber = {2362915}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an:2007035/} }
TY - JOUR AU - Belhachmi, Zakaria AU - Bernardi, Christine AU - Karageorghis, Andreas TI - Mortar spectral element discretization of the Laplace and Darcy equations with discontinuous coefficients JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2007 SP - 801 EP - 824 VL - 41 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2007035/ DO - 10.1051/m2an:2007035 LA - en ID - M2AN_2007__41_4_801_0 ER -
%0 Journal Article %A Belhachmi, Zakaria %A Bernardi, Christine %A Karageorghis, Andreas %T Mortar spectral element discretization of the Laplace and Darcy equations with discontinuous coefficients %J ESAIM: Modélisation mathématique et analyse numérique %D 2007 %P 801-824 %V 41 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2007035/ %R 10.1051/m2an:2007035 %G en %F M2AN_2007__41_4_801_0
Belhachmi, Zakaria; Bernardi, Christine; Karageorghis, Andreas. Mortar spectral element discretization of the Laplace and Darcy equations with discontinuous coefficients. ESAIM: Modélisation mathématique et analyse numérique, Tome 41 (2007) no. 4, pp. 801-824. doi : 10.1051/m2an:2007035. http://www.numdam.org/articles/10.1051/m2an:2007035/
[1] Un schéma de volumes ou éléments finis adaptatif pour les équations de Darcy à perméabilité variable. C.R. Acad. Sci. Paris Série I 333 (2001) 693-698. | Zbl
and ,[2] A priori and a posteriori analysis of finite volume discretizations of Darcy's equations. Numer. Math. 96 (2003) 17-42. | Zbl
, and ,[3] The Mortar finite element method with Lagrangian multiplier. Numer. Math. 84 (1999) 173-197. | Zbl
,[4] Mortar spectral element methods for elliptic equations with discontinuous coefficients. Math. Models Methods Appl. Sci. 12 (2002) 497-524. | Zbl
and ,[5] Spectral Methods, in the Handbook of Numerical Analysis V, P.G. Ciarlet and J.-L. Lions Eds., North-Holland (1997) 209-485.
and ,[6] Spectral element discretizations of the Poisson equation with mixed boundary conditions. Appl. Math. Inform. 6 (2001) 1-29. | Zbl
and ,[7] Adaptive finite element methods for elliptic equations with non-smooth coefficients. Numer. Math. 85 (2000) 579-608. | Zbl
and ,[8] Relèvements de traces préservant les polynômes. C.R. Acad. Sci. Paris Série I 315 (1992) 333-338. | Zbl
, and ,[9] A new nonconforming approach to domain decomposition: the mortar element method, in Collège de France Seminar XI, H. Brezis and J.-L. Lions Eds., Pitman (1994) 13-51. | Zbl
, and ,[10] Discrétisations variationnelles de problèmes aux limites elliptiques, Mathématiques et Applications 45. Springer-Verlag (2004). | MR | Zbl
, and ,[11] Basics and some applications of the mortar element method. GAMM - Gesellschaft für Angewandte Mathematik und Mechanik 28 (2005) 97-123.
, and ,[12] The mortar method in the wavelet context. ESAIM: M2AN 35 (2001) 647-673. | Numdam | Zbl
and ,[13] Solution of a two-dimensional stationary induction heating problem without boundedness of the coefficients. RAIRO Modél. Math. Anal. Numér. 31 (1997) 845-870. | Numdam | Zbl
and ,[14] Finite Element Methods for Navier-Stokes Equations, Theory and Algorithms. Springer-Verlag (1986). | Zbl
and ,[15] Optimal error analysis of spectral methods with emphasis on non-constant coefficients and deformed geometries. Comput. Methods Appl. Mech. Engrg. 80 (1990) 91-115. | Zbl
and ,[16] An -estimate for the gradient of solutions of second order elliptic divergence equations. Ann. Sc. Norm. Sup. Pisa 17 (1963) 189-206. | Numdam | Zbl
,[17] NAG Library Mark 21, The Numerical Algorithms Group Ltd, Oxford (2004).
Cité par Sources :