A posteriori error estimates for a nonconforming finite element discretization of the time-dependent Stokes problem

Abstract

We present aposteriori error estimators for the time-dependent Stokes problem in d , d 2 or 3. Our analysis covers non-conforming finite element approximation (Crouzeix-Raviart's elements) in space and backward Euler's scheme in time. For this discretization, we derive a residual indicator, which uses a spatial residual indicator based on the jumps of normal and tangential deriva- tives of the nonconforming approximation and a time residual indicator based on the jump of broken gradients at each time step. Lower and upper bounds form the main results with minimal assumptions on the mesh. Numerical experiments confirm the theoretical predictions and show the usefulness of these estimators on automatic mesh refinement.