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

Xi Zhang and Minfu Feng

Applied Mathematics and Computation, 2021, vol. 408, issue C

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.

Keywords: Stabilized mixed VEM; Unsteady incompressible Brinkman equations; Projection-based stabilization term; Equal-order polynomials (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:408:y:2021:i:c:s0096300321004148

DOI: 10.1016/j.amc.2021.126325

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