A domain decomposition/finite element method for the numerical simulation of electrolytic cells Original Research Article

In this paper we propose a mathematical formulation for a heat transfer problem with an “interior thin layer” which arises from the thermal modelling of an electrolytic cell. Assuming that the layer is infinitely thin, the problem can be approximated by another one where the temperature presents a jump through an unknown interface, while the heat flux is still a continuous function. It is possible to formulate this free boundary problem as a mixed nonlinear problem the nonlinearity being a multivalued Heaviside function. We prove some results on existence of solution using regularization and fixed point techniques and propose a finite element method to compute a numerical approximation. This approach is combined with the use of a primal formulation in the cathode of the cell through domain decomposition techniques which allows us to use incompatible meshes on the interfaces.