On the full space--time discretization of the generalized Stokes equations: The Dirichlet case

In this work we treat the space-time discretization of the generalized Stokes equations in the case of Dirichlet boundary conditions. We prove error estimates in the case $p\in [\frac{2d}{d+2},\mathrm{\infty })$ that are independent of the degeneracy parameter $\delta \in [0,{\delta }_0]$. For $p\le 2$, our convergence rate is optimal.