For the low-order finite element pair P1P1,based on full domain partition technique,a parallel pressure projection stabilized finite element algorithm for the Stokes equation with nonlinear slip boundary con...For the low-order finite element pair P1P1,based on full domain partition technique,a parallel pressure projection stabilized finite element algorithm for the Stokes equation with nonlinear slip boundary conditions is designed and analyzed.From the definition of the subdifferential,the variational formulation of this equation is the variational inequality problem of the second kind.Each subproblem is a global problem on the composite grid,which is easy to program and implement.The optimal error estimates of the approximate solutions are obtained by theoretical analysis since the appropriate stabilization parameter is chosen.Finally,some numerical results are given to demonstrate the hight efficiency of the parallel stabilized finite element algorithm.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supported by the Natural Science Foundation of China(No.11361016)the Basic and Frontier Explore Program of Chongqing Municipality,China(No.cstc2018jcyjAX0305)Funds for the Central Universities(No.XDJK2018B032).
文摘For the low-order finite element pair P1P1,based on full domain partition technique,a parallel pressure projection stabilized finite element algorithm for the Stokes equation with nonlinear slip boundary conditions is designed and analyzed.From the definition of the subdifferential,the variational formulation of this equation is the variational inequality problem of the second kind.Each subproblem is a global problem on the composite grid,which is easy to program and implement.The optimal error estimates of the approximate solutions are obtained by theoretical analysis since the appropriate stabilization parameter is chosen.Finally,some numerical results are given to demonstrate the hight efficiency of the parallel stabilized finite element algorithm.
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.
