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

IF 1.4 2区数学 Q1 MATHEMATICS

Calcolo Pub Date : 2023-12-29 DOI:10.1007/s10092-023-00560-2

Dmitriy Leykekhman, Boris Vexler

引用次数: 0

Abstract

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 estimate are new even for scalar parabolic problems.

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瞬态斯托克斯问题 Galerkin 解决方案的 $$L^2(I;H^1(\Omega )^d)$$ 和 $$L^2(I;L^2(\Omega )^d)$$ 最佳近似型误差估计值

本文为 $L^2(I;L^2(\Omega )^d)$ 和 $L^2(I;H^1(\Omega )^d)$ 规范下的瞬态斯托克斯问题全离散 Galerkin 解建立了最佳近似型估计。这些估计值填补了瞬态斯托克斯问题误差分析的空白，并有大量应用。分析自然扩展到非均质抛物面问题。最佳类型 $L^2(I;H^1(\Omega ))$ 误差估计即使对于标量抛物问题也是全新的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Calcolo 数学-数学

CiteScore

2.40

自引率

11.80%

发文量

审稿时长

>12 weeks

期刊介绍： Calcolo is a quarterly of the Italian National Research Council, under the direction of the Institute for Informatics and Telematics in Pisa. Calcolo publishes original contributions in English on Numerical Analysis and its Applications, and on the Theory of Computation. The main focus of the journal is on Numerical Linear Algebra, Approximation Theory and its Applications, Numerical Solution of Differential and Integral Equations, Computational Complexity, Algorithmics, Mathematical Aspects of Computer Science, Optimization Theory. Expository papers will also appear from time to time as an introduction to emerging topics in one of the above mentioned fields. There will be a "Report" section, with abstracts of PhD Theses, news and reports from conferences and book reviews. All submissions will be carefully refereed.