Mathematical and numerical analysis of an axisymmetric thermoelectrical problem
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In this talk we analyze a thermoelectrical problem arising from the modeling of induction heating processes. By taking advantage of the cylindrical symmetry, the three-dimensional problem reduces to a two-dimensional one on a meridional section, provided the current density, written in cylindrical coordinates, has only azimuthal component. A variational formulation in appropriate weighted Sobolev spaces is given and existence of solution is proved by applying a fixed-point argument. Moreover, uniqueness and additional regularity is proved under suitable assumptions on the physical coefficients. Finite element approximation combined with a fixed-point iteration are proposed and a priori error estimates are proved. Finally, we present numerical results which allow us to confirm the theoretical estimates and to assess the performance of the proposed method in a physical application.
