Analysis of eddy current formulations in two-dimensional domains with cracks

Abstract

In this paper, the eddy current problem in a two-dimensional conductor containing a crack is studied. The decomposition of the electric field into a piecewise regular part and a singular part deriving from scalar potentials localized at the crack tip and at the crack mouth is proved. At the crack mouth, the electric field is shown to have standard singularities inside the conductor, but presents a singularity outside the conductor that does not belong to the classical L 2 -space. Well-posedness of the E-based model and the A − ψ-formulation of combined potentials are proved and an un-gauged discretization of the latter formulation is discussed.

On a Class of Degenerate Abstract Parabolic Problems and Applications to Some Eddy Current Models

“…hold in a distributional sense. In particular, this confirms that we have indeed solved the original equation (9).…”

“…More specifically, our investigation is inspired by a series of papers by S. Nicaise et al, [11,9,10]. We will employ the theory of evolutionary equations as laid out in Section 1, see [18,16], to analyse the structure of the degenerate eddy current problem.…”