Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations...Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations on a coarse grid, then to solve the resulted residual equations in parallel on a fine grid. This method has low communication complexity. It can be implemented easily. By local a priori error estimate for finite element discretizations, error bounds of the approximate solution are derived. Numerical results are also given to illustrate the high efficiency of the method.展开更多
Based on two-grid discretization,a simplified parallel iterative finite element method for the simulation of incompressible Navier-Stokes equations is developed and analyzed.The method is based on a fixed point iterat...Based on two-grid discretization,a simplified parallel iterative finite element method for the simulation of incompressible Navier-Stokes equations is developed and analyzed.The method is based on a fixed point iteration for the equations on a coarse grid,where a Stokes problem is solved at each iteration.Then,on overlapped local fine grids,corrections are calculated in parallel by solving an Oseen problem in which the fixed convection is given by the coarse grid solution.Error bounds of the approximate solution are derived.Numerical results on examples of known analytical solutions,lid-driven cavity flow and backward-facing step flow are also given to demonstrate the effectiveness of the method.展开更多
Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level met...Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution.展开更多
This paper deals with the two-level Newton iteration method based on the pressure projection stabilized finite element approximation to solve the numerical solution of the Navier-Stokes type variational inequality pro...This paper deals with the two-level Newton iteration method based on the pressure projection stabilized finite element approximation to solve the numerical solution of the Navier-Stokes type variational inequality problem.We solve a small Navier-Stokes problem on the coarse mesh with mesh size H and solve a large linearized Navier-Stokes problem on the fine mesh with mesh size h.The error estimates derived show that if we choose h=O(|logh|^(1/2)H^(3)),then the two-level method we provide has the same H1 and L^(2) convergence orders of the velocity and the pressure as the one-level stabilized method.However,the L^(2) convergence order of the velocity is not consistent with that of one-level stabilized method.Finally,we give the numerical results to support the theoretical analysis.展开更多
基金Project supported by the National Natural Science Foundation of China(No.11001061)the Science and Technology Foundation of Guizhou Province of China(No.[2008]2123)
文摘Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations on a coarse grid, then to solve the resulted residual equations in parallel on a fine grid. This method has low communication complexity. It can be implemented easily. By local a priori error estimate for finite element discretizations, error bounds of the approximate solution are derived. Numerical results are also given to illustrate the high efficiency of the method.
基金supported by the Natural Science Foundation of China(No.11361016)the Project Sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry+1 种基金the Scientific Research Foundation of Southwest University,Fundamental Research Funds for the Central Universities(No.XDJK2014C160,SWU113095)the Science and Technology Foundation of Guizhou Province,China(No.[2013]2212).
文摘Based on two-grid discretization,a simplified parallel iterative finite element method for the simulation of incompressible Navier-Stokes equations is developed and analyzed.The method is based on a fixed point iteration for the equations on a coarse grid,where a Stokes problem is solved at each iteration.Then,on overlapped local fine grids,corrections are calculated in parallel by solving an Oseen problem in which the fixed convection is given by the coarse grid solution.Error bounds of the approximate solution are derived.Numerical results on examples of known analytical solutions,lid-driven cavity flow and backward-facing step flow are also given to demonstrate the effectiveness of the method.
文摘Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution.
基金funded by the National Natural Science Foundation of China under Grant No.10901122 and No.11001205by Zhejiang Provincial Natural Science Foundation of China under Grant No.LY12A01015.
文摘This paper deals with the two-level Newton iteration method based on the pressure projection stabilized finite element approximation to solve the numerical solution of the Navier-Stokes type variational inequality problem.We solve a small Navier-Stokes problem on the coarse mesh with mesh size H and solve a large linearized Navier-Stokes problem on the fine mesh with mesh size h.The error estimates derived show that if we choose h=O(|logh|^(1/2)H^(3)),then the two-level method we provide has the same H1 and L^(2) convergence orders of the velocity and the pressure as the one-level stabilized method.However,the L^(2) convergence order of the velocity is not consistent with that of one-level stabilized method.Finally,we give the numerical results to support the theoretical analysis.
