Error estimates for fully discrete approximation to a free boundary problem in polymer technology (Q1406135)

The discretisation of a free boundary problem that arises in polymer technology is considered. The underlying partial differential equation is the one-dimensional heat equation with homogeneous right-hand side. The full approximation consists of a conforming finite element method in space and the implicit Euler scheme for the time discretisation. The spatial approximation relies upon a domain fixing. The authors prove optimal a priori error estimates in the \(l^{\infty}(L^2)\)- and \(l^{\infty}(H^1)\)-norm for smooth data. Finally, a second-order result is presented for the Crank-Nicolson scheme.