A posteriori analysis of the Chorin–Temam scheme for Stokes equations

Abstract

We consider the Chorin–Temam scheme (the simplest pressure-correction projection method) for the time discretization of an unstationary Stokes problem in D⊂Rd (d=2,3) given μ,f,u0: (P) find (u,p) solution to u|t=0=u0, u|∂D=0 and:(1)∂u∂t−μΔu+∇p=f,divu=0on (0,T)×D. Inspired by the analyses of the Backward Euler scheme performed by C. Bernardi and R. Verfürth, we derive a posteriori estimators for the error on ∇u in L2(0,T;L2(D))-norm. Our investigation is supported by numerical experiments.