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GLOBAL FINITE ELEMENT NONLINEAR GALERKIN METHOD FOR THE PENALIZED NAVIER-STOKES EQUATIONS
作者姓名:Yin-nian  He  Yan-ren  Hou  Li-quan  Mei
作者单位:Faculty of Science,Xi'an Jiaotong University,Xi'an 710049,China
基金项目:Subsidized by the Special Funds for Major State Basic Research Projects G1999032801-07, NSF of China19971067, NSF of Shaanxi P
摘    要:1. IntroductionIn the numerical simulation of the Navier-Stokes equations one encounters three seriousdifficulties in the case of large Reynolds numbers f the treatment of the incomPressibility con-dition divu = 0, the treatment of the noIilinear terms and the large time integration. For thetreatment of the incoInPressibility condition, one use the penalty method in the case of finiteelemellts 1--2l and for the treatmen of the noulinar terms and the large tfor integration, oneuse the nonlin…


GLOBAL FINITE ELEMENT NONLINEAR GALERKIN METHOD FOR THE PENALIZED NAVIER-STOKES EQUATIONS GLOBAL FINITE ELEMENT NONLINEAR GALERKIN METHOD FOR THE PENALIZED NAVIER-STOKES EQUATIONS
Yin-nian He Yan-ren Hou Li-quan Mei.GLOBAL FINITE ELEMENT NONLINEAR GALERKIN METHOD FOR THE PENALIZED NAVIER-STOKES EQUATIONS[J].Journal of Computational Mathematics,2001(6).
Authors:Yin-nian He Yan-ren Hou Li-quan Mei
Abstract:A global finite element nonlinear Galerkin method for the penalized Navier-Stokes equations is presented. This method is based on two finite element spaces XH and Xh, defined respectively on one coarse grid with grid size H and one fine grid with grid size h << H. Comparison is also made with the finite element Galerkin method. If we choose H = O(), E > 0 being the penalty parameter, then two methods are of the same order of approximation. However, the global finite element nonlinear Galerkin method is much cheaper than the standard finite element Galerkin method. In fact, in the finite element Galerkin method the nonlinearity is treated on the fine grid finite element space Xh and while in the global finite element nonlinear Galerkin method the similar nonlinearity is treated on the coarse grid finite element space XH and only the linearity needs to be treated on the fine grid incremeat finite element space Wh. Finally, we provide numerical test which shows above results stated.
Keywords:Nonlinear Galerkin method  Finite element  Penalized Navier-Stokes equations  
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