Some Two Grid Finite Element Methods

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


In this paper, we shall discuss a class of finite element discretization techniques based on two finite element spaces on one coarse and one fine grid. On the fine space, only symmetric positive definite equations need to be solved for a nonsymmetric or indefinite linear equation and only one linear equation need to be solved for a nonlinear equation. It is shown that the coarse grid can be extremely coarse to still achieve the optimal approximation on the fine space for these algorithms. A special nonlinear Galerkin method based on two-grid finite elements is also discussed.

Contributed January 7, 1993.