Ns Equations Upwind Nonlinear Galerkin Finite Element Algorithm And A Posteriori Error Estimates

Conbining two kinds of methods—the upwind finite element method and the nonlinear Galerkin finite element method,which are used to solve Navier-Stokes equations with large Reynolds number, the algorithm to solve Navier-Stokes equations and the posterior error estimation are studied in this paper.First of all, the nonlinear term of the stationary incompressible Navier-Stokes equations in two dimensional domain is dealt by using the homogeneous boundary condition. For the normal triangle mesh, an upwind Galerkin finite element method is presented. Then, the upwind parameter is chosen to satisfy some conditions for the upwind Galerkin finite element method. The trinomial of the Galerkin finite element method has some good properties. The existence and uniqueness of the numerical solution, and the numerical solution with one-order convergence precision are proved. Meanwhile, the certain posterior error estimation is given. Third, Conbining two kinds of method—the upwind finite element method and the nonlinear Gakerkin finite element method,which are used to solve Navier-Stokes equations with large Reynolds number, an upwind nonlinear Galerkin finite element method for the incompressible Navier-Stokes equations is given in. Finally, extending the stationary circumstance to the unstationary one, the convergence of an upwind nonlinear Galerkin finite element method for the unstationary incompressible Navier-Stokes equations is presented and the certain posterior error estimation is also given.