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

Dmitriy Leykekhman; Boris Vexler

doi:10.1007/s10092-023-00560-2

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

Dmitriy Leykekhman, Boris Vexler

Chair of Optimal Control

University of Connecticut

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this paper we establish best approximation type estimates for the fully discrete Galerkin solutions of transient Stokes problem in L²(I; L²(Ω) ^d) and L²(I; H¹(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 L²(I; H¹(Ω)) error estimate are new even for scalar parabolic problems.

Original language	English
Article number	7
Journal	Calcolo
Volume	61
Issue number	1
DOIs	https://doi.org/10.1007/s10092-023-00560-2
State	Published - Mar 2024

Keywords

Best approximation
Discontinuous Galerkin
Error estimates
Finite elements
Fully discrete
Parabolic problems
Stokes problem
Transient Stokes

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10.1007/s10092-023-00560-2

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abstract = "In this paper we establish best approximation type estimates for the fully discrete Galerkin solutions of transient Stokes problem in L2(I; L2(Ω) d) and L2(I; H1(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 L2(I; H1(Ω)) error estimate are new even for scalar parabolic problems.",

keywords = "Best approximation, Discontinuous Galerkin, Error estimates, Finite elements, Fully discrete, Parabolic problems, Stokes problem, Transient Stokes",

author = "Dmitriy Leykekhman and Boris Vexler",

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AU - Leykekhman, Dmitriy

AU - Vexler, Boris

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N2 - In this paper we establish best approximation type estimates for the fully discrete Galerkin solutions of transient Stokes problem in L2(I; L2(Ω) d) and L2(I; H1(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 L2(I; H1(Ω)) error estimate are new even for scalar parabolic problems.

AB - In this paper we establish best approximation type estimates for the fully discrete Galerkin solutions of transient Stokes problem in L2(I; L2(Ω) d) and L2(I; H1(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 L2(I; H1(Ω)) error estimate are new even for scalar parabolic problems.

KW - Best approximation

KW - Discontinuous Galerkin

KW - Error estimates

KW - Finite elements

KW - Fully discrete

KW - Parabolic problems

KW - Stokes problem

KW - Transient Stokes

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M1 - 7

ER -

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

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