Many methods employed in scientific computing are based on a finite element approach. The Galerkin method  for finite elements is discussed, however, other schemes can be implemented as well. The approach of using Galerkin schemes on a topologically based function spaces is shown. In the following, it is implicitly assumed that the differential operators used are linear. Due to the usual solution mechanisms comprising discretization and linearization this does not prohibit the proposed methods from being used for arbitrary problems.