Computational considerations for moving finite element methods

Moving finite element methods allow grid points to follow steep fronts and provide accurate solutions with less computational expense. There are problems that must be recognized in the implementation of this numerical solution technique, but they can be systematically analysed and overcome. Singularity or near singularity of the solution equation set provides specific information about the node motion which can be used to improve the solution. A front tracking and heat conserving solution is presented for a moving boundary problem.