A moving mesh method for the solution of the one-dimensional phase-field equations

A moving mesh method is developed for the numerical solution of one-dimensional phase-change problems modelled by the phase-field equations. The computational mesh is obtained by equidistribution of a monitor function tailored for the functional variation of the phase field in the interfacial region. Existence and uniqueness of the discretised equations using a moving mesh are also established. Numerical results are given for classical and modified Stefan test problems. The numerical algorithm is relatively simple and is shown to be far more efficient than fixed grid methods.