An E-based mixed formulation for a time dependent eddy current problem ∗ Ramiro Acevedo

†

Salim Meddahi

‡

Rodolfo Rodr´ıguez

§

Abstract In this work, we analyze a mixed formulation for a time-dependent eddy current problem formulated in terms of the electric field E. We prove that the problem has a well posed weak formulation. We also show that this formulation admits a well posed saddle point structure when the constraints satisfied by the electric field in the dielectric material is handled by means of a Lagrange multiplier. We use N´ed´elec’s edge elements and standard nodal finite elements to define a semi-discrete Galerkin scheme for this problem. Furthermore, we introduce the corresponding backward-Euler fully-discrete formulation and provide error estimates.

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