Space-Time Finite Elements

The space-time finite element method can be applied if balanced shape functions for different physical variables are provided. Using space-time finite elements, the weak form of the linear momentum is formulated by the principle of virtual velocities and the evolution of the state variables is described by polynomial shape functions.

With the objective of efficiency, the whole space-time domain is split into a set of space-time slabs, that are solved individual for changing boundary- and transition conditions.

Adapting the space-time domain to structural deformations, displayed above, allows for the investigation of fluid-structure interactions in the framework of ALE-formulations.

Applying the space-time finite element method the movements of a free surface between two fluids can be described well by a continuous approximation in both space and time. For example a silo discharge is displayed.