A second order finite element method for the one‐dimensional Stefan problem

We describe a finite element method for the one-dimensional Stefan problem. The elements are quadrilaterals of the space-time plane which are determined at each time-step in relation with the position of the free boundary. The method appears as a generalization of the classical Crank-Nicolson scheme, since it is identical to this scheme in the case of rectangular elements; it has the advantage of providing a simple and accurate determination of the free boundary. Numerical experiments show that the order of accuracy is equal to 2.