An \(\mathbf H\)-based FEM-BEM formulation for a time dependent eddy current problem
A time-dependent eddy current problem posed in the whole space is studied. It is proved that the problem has a well-posed weak formulation. It is also shown that the latter formulation admits a well-posed saddle point structure when the constraint satisfied by the magnetic field in the dielectric medium is handled by means of a Lagrange multiplier. Furthermore, a BEM-FEM formulation of the problem is provided that leads to a semi-discrete Galerkin scheme based on Nédélec's edge elements and Raviart-Thomas elements. Finally, the asymptotic behavior of the error is analyzed in terms of the mesh size parameter.
scientific article; zbMATH DE number 5300745
scientific article