A posteriori estimates for approximations of time-dependent Stokes equations

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 partial differential equation theory can be applied directly, and yield a posteriori estimates that rely on available corresponding estimates for the stationary Stokes equation. Estimates of optimal order in L-infinity(L-2) and L-infinity(H-1) for the velocity are derived for finite-element and finite-volume approximations.