Fully discrete best-approximation-type estimates in L∞ (I;L2(Ω)d) for finite element discretizations of the transient Stokes equations. (25th April 2022)

• Record Type: Journal Article
• Authors: Behringer, Niklas; Vexler, Boris; Leykekhman, Dmitriy
• Is Part Of: IMA journal of numerical analysis. Volume 43:Number 2(2023)
• Page Start: 852
• Page End: 880
• Publication Date: 2022-04-25
• Subjects: transient Stokes -- discontinuous Galerkin method -- finite elements -- best approximation -- pointwise error estimates -- a priori estimates; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/drac009
• Languages: English
• ISSNs: 0272-4979

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.