A-posteriori error estimates for a finite volume method for the Stokes problem in two dimensions

A posteriori estimates for approximations of time-dependent Stokes equations

“…Then we choose χ = I h r, ψ = I h s in (4.21), I h being a Clement-type interpolant onto X h . Using the approximation properties of the interpolant and of the operator Λ h , (4.6), we conclude as in [8] that:…”

“…In the remaining part of this section we show that although Lemma 1.1 is no longer valid as such, U − u h satisfies the necessary orthogonality relations needed to estimate U − u h and (U − u h ) t by applying the stationary a posteriori theory for the finite volume scheme [8]. In fact it is interesting that (u h , p h ) is the stationary finite volume solution to problem (4.10): Lemma 4.2.…”

“…We refer to the works [10,11] for a priori and to [8] for a posteriori estimates for finite volume methods for the stationary Stokes problem.…”

“…It is important for the sequel to note that the finite volume scheme admits a variational formulation similar to the one of finite element case, [8,6,7]. …”

“…Here R K,t denotes the average of R K,t over K. The local error estimators η 0,K in the finite volume case are slightly different than the corresponding in the finite element case: Then, we choose χ as the standard nodal interpolant of z, denoted by I h,N z and ψ = I h s. Following [8] we observe…”