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 Title: On Two Iterative Least-Squares Finite Element Schemes for the Incompressible Navier-Stokes Problem Authors: Chen,MC;Hsieh,PW;Li,CT;Wang,YT;Yang,SY Contributors: 數學研究所 Keywords: ERROR ANALYSIS;EQUATIONS;FORMULATION;FLOW;L-2 Date: 2009 Issue Date: 2010-06-29 19:38:53 (UTC+8) Publisher: 中央大學 Abstract: This paper is mainly devoted to a comparative study of two iterative least-squares finite element schemes for solving the stationary incompressible Navier-Stokes equations with velocity boundary condition. Introducing vorticity as an additional unknown variable, we recast the Navier-Stokes problem into a first-order quasilinear velocity-vorticity-pressure system. Two Picard-type iterative least-squares finite element schemes are proposed to approximate the solution to the nonlinear first-order problem. In each iteration, we adopt the usual L2 least-squares scheme or a weighted L2 least-squares scheme to solve the corresponding Oseen problem and provide error estimates. We concentrate on two-dimensional model problems using continuous piecewise polynomial finite elements on uniform meshes for both iterative least-squares schemes. Numerical evidences show that the iterative L2 least-squares scheme is somewhat suitable for low Reynolds number flow problems, whereas for flows with relatively higher Reynolds numbers the iterative weighted L2 least-squares scheme seems to be better than the iterative L2 least-squares scheme. Numerical simulations of the two-dimensional driven cavity flow are presented to demonstrate the effectiveness of the iterative least-squares finite element approach. Relation: NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION Appears in Collections: [數學研究所] 期刊論文

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