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IMA Journal of Numerical Analysis Advance Access originally published online on July 14, 2007
IMA Journal of Numerical Analysis 2008 28(1):106-120; doi:10.1093/imanum/drm016
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© The author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

The mortar spectral element method in domains of operators. Part II: the curl operator and the vector potential problem

M. Azaïez{dagger}

Laboratoire TREFLE (UMR C.N.R.S. 8508), Site E.N.S.C.P.B., 16 avenue Pey Berland, 33607 Pessac Cedex, France

F. Ben Belgacem{ddagger}

L.M.A.C. (E.A. 2222), Département de Génie Informatique, Université de Technologie de Compiègne, Centre de Recherches de Royallieu, B.P. 20529, 60205 Compiègne Cedex, France

C. Bernardi§

Laboratoire Jacques-Louis Lions, C.N.R.S. and Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France

M. El Rhabi

Realeyes3D S.A., 217 Bureaux de la Colline, 92213 Saint-Cloud Cedex, France

{dagger} Email: azaiez{at}enscpb.fr

{ddagger} Email: faker.ben-belgacem{at}utc.fr

§ Email: bernardi{at}ann.jussieu.fr

Email: melrhabi{at}realeyes3d.fr


  Abstract

The mortar spectral element method is a domain decomposition technique that allows for discretizing second- or fourth-order elliptic equations when set in standard Sobolev spaces. The aim of this paper is to extend this method to problems formulated in the space of square-integrable vector fields with square-integrable curl. We consider the problem of computing the vector potential associated with a divergence-free function in 3D and propose a discretization of it. The numerical analysis of the discrete problem is performed and numerical experiments are presented; they turn out to be in good agreement with the theoretical results.


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