Analysis and approximation of a two-dimensional induction heating problem (opens in new tab)

In this paper, we analyse the existence of solutions and finite element approximation of a steady-state two-dimensional induction heating problem. One of the main difficulties of the problem is its right-hand side which, at a first sight, is only integrable. Using a priori regularity results for the PDEs involved it is shown that the natural weak formulation of the problem can be justified. Then, we study the finite element approximation and pro...