L^2(I;H^1(Ω)) and L^2(I;L^2(Ω)) best approximation type error estimates for Galerkin solutions of transient Stokes problems

04/26/2023

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by   Dmitriy Leykekhman, et al.

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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 estimates seems to be new even for scalar parabolic problems.