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

  • Pyo, Jae-Hong
  • Published : 2009.07.31

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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