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Hybrid mixed formulations for the magnetostatic problem obtained by coupling a conform finite elements method with an integral method

Formulations mixtes hybrides pour le problème de la magnétostatique obtenues en couplant une méthode d'éléments finis conforme avec une méthode intégrale

Abstract : The subject of this thesis is the study of the three-dimensional magnetostatic problem . We present three mixed formulations obtained by coupling a finite elements method to take account of the heterogeneous medium and a boundary integral method to take acount of the homogeneous external medium. For the integral method we use either the Calderon equations , Or Neumann-Dirichlet operator or other integral operator . The use of the elements of edge of Nédélec for the magnetic field, and the elements of face of Raviart for magnetic induction show that the finite element method is conform. Numerical results are given to validate these formulations. The second part related to the comparison of various discretizations for the operator of Poincaré-Steklov. These methods were compared on a formulation of a problem of magnetostatic . Lastly, we proposes discontinuous formulations of the problem of magnetostatic with boundary conditions. It is shown that these formulations are consistent. An hp analysis is carried out and error estimates are obtained.