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. This paper deals with the nite element solution of the eddy cur- rent problem in a bounded conducting domain, crossed by an electric current and subject to boundary conditions appropriate from a physical point of view. Two dieren t cases are considered depending on the boundary data: input cur- rent density ux,or input current intensities. The analysis of the former is an intermediate step for the latter, which is more realistic in actual applications. Weak formulations in terms of the magnetic eld are studied, the boundary conditions being imposed by means of appropriate Lagrange multipliers. The resulting mixed formulations are analyzed depending on the regularity of the boundary data. Finite element methods are introduced in each case and error estimates are proved. Finally, some numerical results to assess the eectiv eness of the methods are reported.

Numerical treatment of realistic boundary conditions for the eddy current problem in an electrode via Lagrange multipliers