Optimal error estimate for semi-discrete gauge-Uzawa method for the Navier-Stokes equations
Bull. Korean Math. Soc. 2009 Vol. 46, No. 4, 627-644
https://doi.org/10.4134/BKMS.2009.46.4.627
Printed July 1, 2009
Jae-Hong Pyo
Kangwon National University
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, Navier-Stokes equation, incompressible fluids
MSC numbers : 65M12, 65M15, 76D05
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