Moving Finite Elements Method for Investigating Stefan Problems

In this paper we will present a detailed study about a specific algorithm based on the moving finite element method (MFEM) to solve Stefan problems in one dimensional space domain. At each time the MFEM determines both nodal amplitudes and nodal positions. Our formulation of MFEM use different meshes associated to each dependent variable and polynomial approximations of arbitrary degree in each finite element. The algorithm we developed to solve nonlinear moving interface problems is based on a mesh decomposition strategy of the spatial domain. In our moving finite element algorithm the spatial domain decomposition is implemented by the introduction of a moving node describing the position of the internal moving interface. This strategy demands an attentive and accurate choice of initial mesh for the spatial domain with an initial length close to zero. Numerical tests are provided to demonstrate the accuracy and robustness of our formulation of the MFEM to solve moving boundary problems. The algorithm developed enables us to achieve accurate results at acceptable CPU times, showing that MFEM is appropriate to solve these kind of problems.