RESIDUAL A POSTERIORI ERROR ESTIMATE OF A NEW TWO-LEVEL METHOD FOR STEADY NAVIER-STOKES EQUATIONS

Residual-based a posteriori error estimate for conforming finite element solutions of incom-pressible Navier-Stokes equations,which is computed with a new two-level method that is differentfrom Volker John,is derived.A posteriori error estimate contains additional terms in comparison tothe estimate for the solution obtained by the standard finite element method.The importance of theadditional terms in the error estimates is investigated by studying their asymptotic behavior.For opti-mal scaled meshes,these bounds are not of higher order than the convergence of discrete solution.Thetwo-level method aims to solve the nonlinear problem on a coarse grid with less computational work,then to solve the linear problem on a fine grid,which is superior to the usual finite element methodsolving a similar nonlinear problem on the fine grid.