We prove that the discrete Laplace operator has a bounded $ H^\infty $-calculus,
independent of the spatial mesh size. As an application, we obtain the discrete stochastic …

We establish resolvent estimates in L q spaces for the Stokes operator in a bounded C 1
domain Ω in R d. As a corollary, it follows that the Stokes operator generates a bounded …

This paper develops L pL q decay estimates of the gradient of the Stokes semigroup (T (t))
t≥ 0 generated by the negative of the Stokes operator in exterior Lipschitz domains Ω⊂ R n …

In this work we consider the two dimensional instationary Navier–Stokes equations with
homogeneous Dirichlet/no-slip boundary conditions. We show error estimates for the fully …

This work studies different physically motivated mathematical models. For discrete periodic
Schrödinger operators, we derive sufficient conditions on the applicability of the finite section …

Consider the three-dimensional Navier--Stokes flow past a moving rigid body $\mathscr
{O}\subset\mathbb {R}^ 3$ with prescribed translational and angular velocities, where …

This book is a revised, updated, and augmented version of the out-of-print classic book
Finite Element Methods for Navier-Stokes Equations by Girault and Raviart published by …

We establish resolvent estimates in spaces of bounded solenoidal functions for the Stokes
operator in a bounded domain $\Omega $ in $ R^ d $ under the assumptions that $\Omega …