A Crank–Nicolson Type Space–Time Finite Element Method for Computing on Moving Meshes

In this paper, a space–time finite element method for evolution problems that is second-order accurate in both space and time is proposed. For convection dominated problems, the elements may be aligned along the characteristics in space–time, which results in a Crank–Nicolson method along the characteristics. The method is also suitable as an alternative to other moving mesh methods for problems in deforming domains. Numerical examples dealing with diffusion and convection are given.