Ana Alonso Rodríguez, Enrico Bertolazzi, Alberto Valli
New variational formulations are devised for the curl--div system, and the corresponding finite element approximations are shown to converge. Curl--free and divergence--free finite elements are employed for discretizing the problem.
Ana Alonso Rodríguez, Salim Meddahi, Alberto Valli
We introduce and analyze a discontinuous Galerkin FEM/BEM method for a time-harmonic eddy current problem written in terms of the magnetic field. We use nonconforming Nédélec finite elements on a partition of the interior domain coupled with continuous boundary elements on the transmission interface. We prove quasi-optimal error estimates in the energy norm.
Ana Alonso Rodríguez, Salim Meddahi, Alberto Valli
We introduce and analyze a discontinuous Galerkin method for a time-harmonic eddy current problem formulated in terms of the magnetic field. The scheme is obtained by putting together a DG method for the approximation of the vector field variable representing the magnetic field in the conductor and a DG method for the Laplace equation whose solution is a scalar magnetic potential in the insulator. The transmission conditions linking the two problems are taken into account weakly in the global discontinuous Galerkin scheme. We prove that the numerical method is uniformly stable and obtain quasi-optimal error estimates in the DG-energy norm.