%0 Generic
%A Besier, Michael
%A Wollner, Winnifried
%D 2010
%F heidok:11125
%K space-time finite elements , dynamically changing meshes , incompressible fluids , pressure approximation , discontinuous Galerkin method in time
%R 10.11588/heidok.00011125
%T On the Dependence of the Pressure on the Time Step in Incompressible Flow Simulations on Varying Spatial Meshes
%U https://archiv.ub.uni-heidelberg.de/volltextserver/11125/
%X Subject of this paper is an analysis of the behavior of the pressure on dynamically changing spatial meshes during the computation of nonstationary incompressible flows. In particular, we are concerned with discontinuous Galerkin finite element discretizations in time. Here it is observed that whenever the spatial mesh is changed between two time steps the pressure in the next time step will diverge with order $k^{-1}$. We will proof that this behavior is due to the fact, that discrete solenoidal fields lose this property under changes of the spatial discretization. In addition we will numerically study the fractional-step-$theta$ scheme, and discuss why the divergence is not observed when using this time discretization. Finally we will derive a possible way to circumvent this problem.