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 timedependent 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∞(L2) and L∞(H1) for the velocity are derived for finite-element and finite-volume approximations.