Based on fully overlapping domain decomposition,three parallel finite element algorithms for time-dependent Navier-Stokes equations are proposed.Basic idea of algorithms is to discretize spatial space with fully overlapping domain decomposition technique,and then to solve ordinary differential equations with respect to time independently in backward Euler scheme on overlapped subdomains.The nonlinear convective term is dealt with semi-and fully-implicit schemes,respectively.In these algorithms,each subproblem is a global problem with vast majority of degrees of freedom associated with a particular subdomain that is responsible for,which allows algorithms to be implemented easily with low communication costs.Numerical test illustrates efficiency and good parallel performance of the algorithms.

Here a practicable algorithm about the nonlinear Galerkin finite element algorithm is presented for the two-dimensional steady incompressible equations of Navier-stokes type is presented (or discassed),also the conver-gence and regularity of the numerical solution are analysed.If the grid parameter H and the finner grid parameter h(h1/2),the present algorithm has convergence rate of the same order as the standard Galerkin finite element algorithm.However,this algorithm is simpler than the Galerkin algorithm and can save a large amount of computational time.Finally,the numerical test is provided,which shows that the above conclusion is are true.