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In this work we treat the space-time discretization of the generalized Stokesequations in the case of Dirichlet boundary conditions. We prove errorestimates in the case $p\in[\frac{2d}{d+2},\infty)$ that are independent of thedegeneracy parameter $\delta\in[0,\delta_0]$. For $p\leq 2$, our convergencerate is optimal.

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