Two-grid finite-element schemes for the steady Navier-Stokes problem in polyhedra. (English) Zbl 0997.76043
Summary: We discretize the steady Navier-Stokes system on a three-dimensional polyhedron by finite element schemes defined on two grids. At the first step, the fully nonlinear problem is solved on a coarse grid, with mesh size . At the second step, the problem is linearized by substituting into the nonlinear term the velocity computed at step one, and the linearized problem is solved on a fine grid with mesh size . This approach is motivated by the fact that the contribution of to the error analysis is measured in the norm, and thus, for the lowest-degree elements on a Lipschitz polyhedron, is of the order of . Hence, an error of the order of can be recovered at the second step, provided . When the domain is convex, a similar result can be obtained with . Both results are valid in two dimensions.
|76M10||Finite element methods (fluid mechanics)|
|76D05||Navier-Stokes equations (fluid dynamics)|
|65N15||Error bounds (BVP of PDE)|
|65N30||Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)|
|65N55||Multigrid methods; domain decomposition (BVP of PDE)|