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http://dx.doi.org/10.4134/BKMS.2009.46.4.627

OPTIMAL ERROR ESTIMATE FOR SEMI-DISCRETE GAUGE-UZAWA METHOD FOR THE NAVIER-STOKES EQUATIONS  

Pyo, Jae-Hong (DEPARTMENT OF MATHEMATICS KANGWON NATIONAL UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.46, no.4, 2009 , pp. 627-644 More about this Journal
Abstract
The gauge-Uzawa method which has been constructed in [11] is a projection type method to solve the evolution Navier-Stokes equations. The method overcomes many shortcomings of projection methods and displays superior numerical performance [11, 12, 15, 16]. However, we have obtained only suboptimal accuracy via the energy estimate in [11]. In this paper, we study semi-discrete gauge-Uzawa method to prove optimal accuracy via energy estimate. The main key in this proof is to construct the intermediate equation which is formed to gauge-Uzawa algorithm. We will estimate velocity errors via comparing with the intermediate equation and then evaluate pressure errors via subtracting gauge-Uzawa algorithm from Navier-Stokes equations.
Keywords
projection method; gauge method; Uzawa method; gauge-Uzawa method; avier-Stokes equation; incompressible fluids;
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