Iterative methods in penalty finite element discretizations for the Steady Navier–Stokes equations

[1]  Vivette Girault,et al.  Finite Element Methods for Navier-Stokes Equations - Theory and Algorithms , 1986, Springer Series in Computational Mathematics.

[2]  P. Hood,et al.  A numerical solution of the Navier-Stokes equations using the finite element technique , 1973 .

[3]  Yinnian He,et al.  Two-level Stabilized Finite Element Methods for the Steady Navier–Stokes Problem , 2005, Computing.

[4]  M. Marion,et al.  Nonlinear Galerkin methods and mixed finite elements: two-grid algorithms for the Navier-Stokes equations , 1994 .

[5]  Jie Shen,et al.  On error estimates of the penalty method for unsteady Navier-Stokes equations , 1995 .

[6]  U. Ghia,et al.  High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method , 1982 .

[7]  Wing Kam Liu,et al.  Finite Element Analysis of Incompressible Viscous Flows by the Penalty Function Formulation , 1979 .

[8]  Yinnian He,et al.  Convergence of three iterative methods based on the finite element discretization for the stationary Navier–Stokes equations☆ , 2009 .

[9]  R. Rannacher,et al.  Finite element approximation of the nonstationary Navier-Stokes problem. I : Regularity of solutions and second-order error estimates for spatial discretization , 1982 .

[10]  Noboru Kikuchi,et al.  Finite element methods for constrained problems in elasticity , 1982 .

[11]  Xiliang Lu,et al.  Error estimate of the P1 nonconforming finite element method for the penalized unsteady Navier-Stokes equations , 2010, Numerische Mathematik.

[12]  R. Temam Une méthode d'approximation de la solution des équations de Navier-Stokes , 1968 .

[13]  Graham F. Carey,et al.  Convergence of iterative methods in penalty finite element approximation of the Navier-Stokes equations , 1987 .

[14]  Yinnian He,et al.  A simplified two-level method for the steady Navier–Stokes equations , 2008 .

[15]  Jian Li,et al.  A penalty finite element method based on the Euler implicit/explicit scheme for the time-dependent Navier-Stokes equations , 2010, J. Comput. Appl. Math..

[16]  Yinnian He,et al.  Optimal error estimate of the penalty finite element method for the time-dependent Navier-Stokes equations , 2005, Math. Comput..

[17]  Jean-Michel Ghidaglia,et al.  Attractors for the penalized Navier-Stokes equations , 1988 .

[18]  Yinnian He,et al.  Two‐level Newton iterative method for the 2D/3D steady Navier‐Stokes equations , 2012 .

[19]  Ramon Codina,et al.  An iterative penalty method for the finite element solution of the stationary Navier-Stokes equations , 1993 .

[20]  Jie Shen,et al.  On error estimates of some higher order projection and penalty-projection methods for Navier-Stokes equations , 1992 .

[21]  Peter Oswald On a hierarchical basis multilevel method with nonconforming P1 elements , 1992 .