A posteriori error estimates for a nonconforming finite element discretization of the time-dependent Stokes problem, II: Analysis of the spatial estimator

Abstract

We complete the analysis of our a posteriori error estimators for the time-dependent Stokes problem in Rd, 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 derived in part I of this paper [J. Numer. Math. (2007) 15, No. 2, 137–162] a residual indicator, which uses a spatial residual indicator based on the jumps of normal and tangential derivatives of the nonconforming approximation and a time residual indicator based on the jump of broken gradients at each time step. In this second part we prove some analytical tools, and derive the lower and upper bounds of the spatial estimator.