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

Mjedi Azaïez (1) , Faker Ben Belgacem (2) , Christine Bernardi (3) , Mohammed El Rhabi (4)

1 TREFLE - Transferts, écoulements, fluides, énergétique
2 LMAC - Laboratoire de Mathématiques Appliquées de Compiègne
3 LJLL - Laboratoire Jacques-Louis Lions
4 Realeyes3D SA

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.

Domaines: Analyse numérique [math.NA]

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, 2008, 187 (3), pp.405-433. ⟨10.1007/s10231-007-0049-y⟩. ⟨hal-00112170⟩