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Published in: Calcolo 4/2021

01-12-2021

Lowest order virtual element approximations for transient Stokes problem on polygonal meshes

Authors: N. Verma, S. Kumar

Published in: Calcolo | Issue 4/2021

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Abstract

In this paper, we discuss and analyze virtual element approximations for the nonstationary Stokes problem on polygonal meshes. The proposed scheme is based on pressure-velocity formulations, and the virtual element spaces associated with velocity and pressure are constructed in a way that they obey the discrete inf-sup (LBB) condition. The spatial discretization for velocity is based on piecewise linear polynomials as well as non-linear functions, and the pressure approximation is relied on discontinuous piecewise constant polynomials, whereas a backward Euler method is employed for the time discretization. By introducing suitable energy and \(L^2\) projection operators, the optimal error estimates are established in \(H^1\) and \(L^2\) norms for both semi and fully discrete schemes under the minimal regularity assumptions on continuous solutions. Moreover, several numerical experiments are conducted to validate the obtained theoretical rate of convergence and exhibit the performance of the proposed scheme.
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Metadata
Title
Lowest order virtual element approximations for transient Stokes problem on polygonal meshes
Authors
N. Verma
S. Kumar
Publication date
01-12-2021
Publisher
Springer International Publishing
Published in
Calcolo / Issue 4/2021
Print ISSN: 0008-0624
Electronic ISSN: 1126-5434
DOI
https://doi.org/10.1007/s10092-021-00440-7

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