The aim of this paper is to present a general algorithm for solving the nonlinear operator equations in a Hilbert space, namely the k -order Taylor expansion algorithm, k¿1 . The standard Galerkin method can be viewed as the 1-order Taylor expansion algorithm; while the optimum nonlinear Galerkin method can be viewed as the 2-order Taylor expansion algorithm. The general algorithm is then applied to the study of the numerical approximations for the steady Navier-Stokes equations. Finally, the theoretical analysis and numerical experiments show that, in some situations, the optimum nonlinear Galerkin method provides higher convergencerate than the standard Galerkin method and nonlinear Galerkin method.
|Journal||Acta Mathematica Sinica|
|Publication status||Published - 1998|