The problem of simulations in three dimensions comes on the one hand from the enormous memory consumption and the resulting long calculation times and on the other hand from the poor numeric behavior of the complete system since e.g. the linear Galerkin finite element discretization of the Laplace operator produce non positive stiffness coefficients for internal element edges[Put98]. That is, among others, a reason why development of simulation tools in three dimensions is much more complicated since the same models often do not behave in the same manner that is known from the simpler lower dimensional experiences.
The following calculations show some examples in three dimensions that were calculated using the model presented in the previous section.