We consider stabilized mixed hp-discontinuous Galerkin methods for the discretization of the Stokes problem in three-dimensional polyhedral domains. The methods are stabilized with a term penalizing the pressure jumps. For this approach it is shown that IQk-IQk and IQk-IQk-1 elements satisfy a generalized inf-sup condition on geometric edge and boundary layer meshes that are refined anisotropically and non quasi-uniformly towards faces, ...

Galerkin discretizations of integral equations in $\mathbb{R}^d$ require the evaluation of integrals $ I = \int_{S^{{(1)}}}$ $ \int_{S^{{(2)}}}$ $g(x,y)dydx$ where $S^{{(1)}}$, $S^{{(2)}}$ are $d$-simplices and $g$ has a singularity at $x=y$. We assume that g is Gevrey smooth for $x \neq y$ and satisfies bounds for the derivatives which allow algebraic singularities at $x = y$. This holds for kernel functions commonly occuring in integral ...