Mixed finite element method for a single phase Stefan problem (Q1611527)

A mixed finite element method is applied to a one-dimensional single phase Stefan problem using a front fixing technique. The free boundary of the problem is transformed by a Landau type transformation into a coupled system of a parabolic equation with a quadratic nonlinear term in a fixed domain and two ordinary differential equations. A mixed weak formulation and a continuous time Galerkin method are introduced. For the semi-discrete case optimal error estimates in \(L^2\), \(H^1\) and \(H^2\) norms are given.