Fully discrete best-approximation-type estimates in L∞ (I;L2(Ω)d) for finite element discretizations of the transient Stokes equations-Reference-Cited by-同舟云学术

Fully discrete best-approximation-type estimates in L∞ (I;L2(Ω)d) for finite element discretizations of the transient Stokes equations

Published:2022-04-25 Issue:2 Volume:43 Page:852-880
ISSN:0272-4979
Container-title:IMA Journal of Numerical Analysis
language:en
Short-container-title:

Author:

Behringer Niklas¹,Vexler Boris¹,Leykekhman Dmitriy²

Affiliation:

1. Center for Mathematical Sciences, Technical University of Munich , 85748 Garching by Munich, Germany

2. Department of Mathematics, University of Connecticut , Storrs, CT 06269, USA

Abstract

Abstract In this article, we obtain an optimal best-approximation-type result for fully discrete approximations of the transient Stokes problem. For the time discretization, we use the discontinuous Galerkin method and for the spatial discretization we use standard finite elements for the Stokes problem satisfying the discrete inf-sup condition. The analysis uses the technique of discrete maximal parabolic regularity. The results require only natural assumptions on the data and do not assume any additional smoothness of the solutions.

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics,Computational Mathematics,General Mathematics

Link

https://academic.oup.com/imajna/article-pdf/43/2/852/49629915/drac009.pdf

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