A fixed grid finite element method for nonlinear diffusion problems with moving boundaries

A comprehensive formulation for a class of diffusion problems with non-linear conductivities is derived by unifying and combining the freezing index and Kirchhoff transformation concepts. The transformed equations have appropriate continuity characteristics across the unknown moving boundary. The applicability of the fixed grid algorithm for the total solution domain is, accordingly, demonstrated. Associated finite element formulations and solution procedures for the transformed equations are detailed. In addition, selected numerical results for single and two phase Stefan type problems as well as fluid flow in a prescribed cavity are presented for solution verification and illustration.