Error Estimates on a New Nonlinear Galerkin Method Based
on a Two Grid Finite Elements

Martine Marion

Jinchao Xu
Deparpartment of Mathematics
Penn State University
University Park, PA 16802


A new nonlinear Galerkin method based on finite element discretization is presented in this paper for a class of second order nonlinear parabolic equations. The new scheme is based on two different finite element spaces defined respectively on one coarse grid with grid size H and one fine grid with grid size h << H. Nonlinearity and time dependence are both treated on the coarse space and only a fixed stationary equation needs to be solved on the fine space at each time. With linear finite element discretizations, it is proved that the difference between the new nonlinear Galerkin solution and the standard Galerkin solution in H1(Omega) norm is of the order of H3.

Contributed January 7, 1993.