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Mathematics in Computer Science

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31.03.2020

On the \({ H}^{1}\) Conforming Virtual Element Method for Time Dependent Stokes Equation

verfasst von: Dibyendu Adak, Sundararajan Natarajan

Erschienen in: Mathematics in Computer Science | Ausgabe 1/2021

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Abstract

In this paper, we present a virtual element method for the time-dependent Stokes equation by employing a mixed formulation involving the velocity and the pressure as primitive variables. The velocity is approximated using the \(H^1\) conforming virtual element and the pressure is approximated by the discontinuous piecewise polynomial. In order to approximate the non-stationary part with optimal order of convergence, we need to compute the \(L^2\) projection operator of the full order k. In view of this requirement, we modify the velocity space keeping the same dimension. The virtual space is discrete inf-sup stable for \(k \ge 2\) and non-divergence free. We estimate the optimal order of convergence for the velocity and the pressure.

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Titel: On the Conforming Virtual Element Method for Time Dependent Stokes Equation
verfasst von: Dibyendu Adak
Sundararajan Natarajan
Publikationsdatum: 31.03.2020
Verlag: Springer International Publishing
Erschienen in: Mathematics in Computer Science / Ausgabe 1/2021
Print ISSN: 1661-8270
Elektronische ISSN: 1661-8289
DOI: https://doi.org/10.1007/s11786-020-00473-1

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