Numerical solutions for a Stefan problem

Abstract

The initial version of a Stefan problem is the melting of a semi-infinite sheet of ice. This problem is described by a parabolic partial differential equation along with two boundary conditions on the moving boundary which are used to determine the boundary itself and complete the solution of the differential equation. In this paper firstly, we use variable space grid method, boundary immobilisation method and isotherm migration method to get rid of the trouble of the Stefan problem. Then, collocation finite element method based on cubic B-spline bases functions is applied to model problem. The numerical schemes of finite element methods provide a good numerical approximation for the model problem. The numerical results show that the present results are in good agreement with the exact ones.

Keywords

• Stefan problems,variable space grid method,boundary immobilisation method,isotherm migration method

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