To allow for time-depended problems to be solved completely with the finite element method, special elements are necessary, that can be integrated as well spatially as with respect to time. This means a lot of additional work, although the finite element method itself is very time-consuming. The result is that the already complex solving strategy becomes even more abstract and more difficult to understand. That is why a so-called semi-discrete method is used in many applications of the finite element method (e.g. in RMA2). In this case it is assumed that it is possible to separate the dependency on time from the spatial variation. In the semi-discrete method just like for the steady problem, the weak form is derived, which in our case can be expressed as: