Error estimates on a new nonlinear Galerkin method based on two-grid finite elements. (English) Zbl 0853.65092

Marion, Martine; Xu, Jinchao

SIAM J. Numer. Anal. 32, No. 4, 1170-1184 (1995).

This paper presents a new nonlinear Galerkin method for semilinear parabolic equations. The new scheme is based on two different finite element spaces defined respectively on one coarse grid and one fine grid. With linear finite element discretization, the difference between the new nonlinear Galerkin solution and the standard Galerkin solution is estimated.

Reviewer: Q.Duan (Mountain View)

MSC:

65M15	Error bounds for initial value and initial-boundary value problems involving PDEs
35K55	Nonlinear parabolic equations
65M55	Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
65M60	Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs

Keywords:

multigrid; nonlinear Galerkin method; semilinear parabolic equations; finite element