An adaptive Galerkin method for the time-dependent complex Schrödinger equation

In this article, we consider finite element approximations using continuous Galerkin schemes in time and space by adaptive mesh balancing both errors. To get this balance, we adapt the dual weighted residual method used for wave equations and estimates of error indicators for adaptive space-time finite element discretization. The results show how important is dynamic refinement to control the degrees of freedom in space.