A POSTERIORI ESTIMATES FOR APPROXIMATIONS OF TIME DEPENDENT STOKES EQUATIONS

Abstract. In this paper we derive a posteriori error estimates for space discrete approximations of the time dependent Stokes equations. By using an appropriate Stokes reconstruction operator we are able to write an auxiliary error equation in pointwise form that satisfies the exact divergence free condition. Thus standard energy estimates from pde theory can be applied directly to yield a posteriori estimates that rely on available corresponding estimates of the stationary Stokes equation. Estimates of optimal order in L∞(L2) and in L∞(H1) for the velocity are derived for finite element and finite volume approximations. 1