A free-Lagrange finite element method using space-time elements Original Research Article

We consider the construction and implementation of a `free-Lagrangeʹ finite element method, where local mesh modifications can be introduced during computation. The method is based on the use of space-time oriented meshes, with the space-time elements aligned along the (approximate) characteristics. In particular, we address the problem of mass conservation in transferring data between different grids. Numerical examples range from convection–diffusion to incompressible flow in domains with moving parts.