REGULARITY CONSTANTS OF THE STOKES PROBLEM: APPLICATION TO FINITE-ELEMENT METHODS ON CURVED DOMAINS

Abstract

For bounded smooth domains, we study how the solution of the Stokes problem is bounded in terms of the data when the domain changes. We show that standard bounds for a fixed domain hold with the same constant for wide classes of domains. This is done by first reviewing the original results of Cattabriga and then, in terms of geometric properties of the domains, by specifying when to apply Cattabriga's intermediate results. We do the same with standard strong extension and trace theorems.We apply these results to an elegant technique of analysis due to Wahlbin to overcome the disparity between a curved domain and the domains where finite-element computations are carried out in practice without resorting to numerical quadrature.