Doctoral position in in Adaptive Mesh Refinement in Space-time Finite Element Meshes (Germany)
Many application areas in process and material engineering require the modelling and simulation of moving phase interfaces. The filling phase in injection moulding or high-pressure die casting can serve as examples.
The main aim of the current project is the development and implementation of an adaptive refinement scheme in space, but particularly also in time, in the context of a space-time finite element discretization.
Compared to conventional methods that use separate 3D-grids in space and 1D-grids in time successively, the aim is to refine adaptively in time based on 4D-space-time grids. This approach will allow for local refinement in areas that require increased accuracy. This means that different parts of the computational domain use varying time-step sizes. It is to be expected that such an approach can improve the accuracy of the solution by an order of magnitude at constant mesh resolution.