Optimal error estimate for semi-discrete gauge-Uzawa method for the Navier-Stokes equations
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초록
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.
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.
참고문헌 (18)
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