Rommel Bustinza, Bibiana López-Rodríguez, Mauricio Osorio:
An a priori error analysis of an HDG method for an eddy current problem
This paper concerns itself with the development of an a priori error analysis of an eddy current problem when applying the well known Hybridizable discontinuous Galerkin (HDG) method. Up to the authors knowledge, this kind of theoretical result has not been proved for this kind of problems. We consider non trivial domains and heterogeneous media which contain conductor and insulating materials. When dealing with these domains, it is necessary to impose the divergence-free condition explicitly in the insulator, what is done by means of a suitable Lagrange multiplier in that material. In the end, we deduce an equivalent HDG formulation that includes as unknowns the tangential and normal trace of a vector eld. This represents a reduction in the degrees of freedom when compares with the standard DG methods. For this scheme we conduct a consistency and local conservative analysis as well as its unique solvability. After that, we introduce suitable projection operators that help us to deduce the expected a priori error estimate, which provides estimated rates of convergence when additional regularity on the exact solution is assumed.