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 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 ∞ (L 2 ) and L ∞ (H 1 ) for the velocity are derived for finite-element and finite-volume approximations.
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