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

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 ap...

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Veröffentlicht in:Calcolo 2024, Vol.61 (1)
Hauptverfasser: Leykekhman, Dmitriy, Vexler, Boris
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Error analysis
Estimates
Galerkin method
Mathematical analysis
Mathematics
Mathematics and Statistics
Numerical Analysis
Theory of Computation
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Zusammenfassung: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.
ISSN:0008-0624
1126-5434
DOI:10.1007/s10092-023-00560-2