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

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.he 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 dimension 3 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 coherency with the theoretical results.
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Submitted on : Friday, November 10, 2006 - 9:50:55 AM
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Mjedi Azaïez, Faker Ben Belgacem, Christine Bernardi, Mohammed El Rhabi. The mortar spectral element method in domains of operators Part II: The curl operator and the vector potential problem. Annali di Matematica Pura ed Applicata, Springer Verlag, 2008, 187 (3), pp.405-433. ⟨10.1007/s10231-007-0049-y⟩. ⟨hal-00112170⟩

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