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arXiv:2304.13839 [math.NA]AbstractReferencesReviewsResources

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

Dmitriy Leykekhman, Boris Vexler

Published 2023-04-26Version 1

In this paper we establish best approximation type estimates for the fully discrete Galerkin solutions of transient Stokes problem in $L^2(I;L^2(\Omega)^d)$ and $L^2(I;H^1(\Omega)^d)$ 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 $L^2(I;H^1(\Omega))$ error estimates seems to be new even for scalar parabolic problems.

Comments: arXiv admin note: substantial text overlap with arXiv:2107.11051
Categories: math.NA, cs.NA
Subjects: 65N30
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