In Chapter 1 we presented basic ideas for the reduction of boundary value problems of the
Laplacian to various forms of boundary integral equations based on the direct approach …

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 …

In this paper we are concerned with two topics: the formulation and analysis of the
eigenvalue problem for the curl\nolimits curl operator in a multiply connected domain and its …

In this paper we analyze the coupling of local discontinuous Galerkin (LDG) and boundary
element methods as applied to linear exterior boundary value problems in the plane. As a …

In this paper, we study a time-dependent eddy current problem posed in the whole space.
We prove that the problem has a well-posed weak formulation. We also show that the latter …

We propose a new implementation of the finite element approximation of eddy current
problems using, as the principal unknown, the magnetic field. In the non-conducting region a …

In this paper we analyse a mixed finite-element method and boundary-element method
coupling for a time-dependent eddy current problem posed in the whole space and …

The aim of this work is to show an abstract framework to analyze the numerical
approximation for a family of linear degenerate parabolic mixed equations by using a finite …

The three-dimensional eddy current time-dependent problem is considered. We formulate it
in terms of two variables, one lying only on the conducting domain and the other on its …

This paper deals with finite element methods for the numerical solution of the eddy current
problem in a bounded conducting domain crossed by an electric current, subjected to …