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A projection-based stabilized virtual element method for the unsteady incompressible Brinkman equations

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  • Zhang, Xi
  • Feng, Minfu

Abstract

This paper is devoted to a stabilized mixed virtual element method (mixed VEM) for the unsteady incompressible Brinkman equations. We employ the pairs of C0-conforming virtual element spaces containing the “equal-order” polynomials to approximate the velocity and pressure variables, and replace the time derivative by a backward Euler difference quotient. The numerical stability is guaranteed with a new projection-based stabilization term, which is simple without the projection of second derivatives or the coupling terms. We also establish the error estimates for both the semi-discrete and fully-discrete schemes with respect to the viscosity coefficient. Finally, we carry out several numerical experiments to validate the theoretical analysis.

Suggested Citation

  • Zhang, Xi & Feng, Minfu, 2021. "A projection-based stabilized virtual element method for the unsteady incompressible Brinkman equations," Applied Mathematics and Computation, Elsevier, vol. 408(C).
    • Handle: RePEc:eee:apmaco:v:408:y:2021:i:c:s0096300321004148
    DOI: 10.1016/j.amc.2021.126325
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    References listed on IDEAS

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    1. Zhang, Baiju & Feng, Minfu, 2018. "Virtual element method for two-dimensional linear elasticity problem in mixed weakly symmetric formulation," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 1-25.
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