L2(I;H1(Ω)d) and L2(I;L2(Ω)d) best approximation type error estimates for Galerkin solutions of transient Stokes problems.

In this paper we establish best approximation type estimates for the fully discrete Galerkin solutions of transient Stokes problem in L 2 (I ; L 2 (Ω) d) and L 2 (I ; H 1 (Ω) d) norms. These estimates fill the gap in the error analysis of the transient Stokes problems and have a number of applications. The analysis naturally extends to inhomogeneous parabolic problems. The best type L 2 (I ; H 1 (Ω)) error estimate are new even for scalar parabolic problems. [ABSTRACT FROM AUTHOR]