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A finite element method based on time dependent basis functions is presented for solving a two phase Stefan problem for the heat equation in one space dimension. The stability and the convergence of the method are studied, and a numerical example is given. § I, A Two Phase Stefan Problem In One Space Dimension This paper is concerned with a finite element solution of the following two phase Stefan problem in one space dimension for the heat equation. Given the data Qi(t), Qz (f) , f\ (x) , f2 (x) and b, find functions U i ( x 9 f ) 9 u2(x9t) and x = s(t) in 0<.r<L, 0<*^T, such that a. dt 9-r s(t)<x<L, 0-O^ (1.2) » . ( L , t ) = g . ( t ) , (1.3) .s(0) = £, 0 , b L,

A finite element method for solving the two phase Stefan problem in one space dimension