A Galerkin method for Stefan problems

摘要

Stefan problems are described by a parabolic partial-differential equation, along with two boundary conditions on a moving boundary, which is to be determined as part of the solution. The purpose of this paper is to develop a finite-element method for the solution of a one-dimensional Stefan problem. First, a coordinate transformation is used to transform the changing physical domain into a fixed computational domain. Then, the weak or Galerkin formulation of the initial boundary value problem is used to reduce it to a system of initial-value problems in ordinary differential equations. Several finite-difference marching methods are used to solve the resulting initial-value problems. The method is developed and illustrated using the Stefan problem concerning the heat transfer in an ice-water medium. The computational results are in very good agreement with the results produced earlier by several authors.