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

Acevedo, Ramiro; Meddahi, Salim; Rodríguez, Rodolfo

doi:10.1090/S0025-5718-09-02254-6

An $\boldsymbol {E}$-based mixed formulation for a time-dependent eddy current problem
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by Ramiro Acevedo, Salim Meddahi and Rodolfo Rodríguez PDF

Math. Comp. 78 (2009), 1929-1949 Request permission

Abstract:

In this paper, we analyze a mixed form of a time-dependent eddy current problem formulated in terms of the electric field $\boldsymbol {E}$. We show that this formulation admits a well-posed saddle point structure when the constraints satisfied by the primary unknown in the dielectric material are handled by means of a Lagrange multiplier. We use Nédélec edge elements and standard nodal finite elements to define a semi-discrete Galerkin scheme. Furthermore, we introduce the corresponding backward-Euler fully-discrete formulation and prove error estimates.

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