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

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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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  1. Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, 600036, India

    Dibyendu Adak & Sundararajan Natarajan

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  1. Dibyendu Adak
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  2. Sundararajan Natarajan
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Correspondence to Sundararajan Natarajan.

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Adak, D., Natarajan, S. On the \({ H}^{1}\) Conforming Virtual Element Method for Time Dependent Stokes Equation. Math.Comput.Sci. 15, 135–154 (2021). https://doi.org/10.1007/s11786-020-00473-1

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  • DOI: https://doi.org/10.1007/s11786-020-00473-1

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