DEPARTMENT OF MATHEMATICS Local and Parallel Finite Element Algorithms Based on Two-Grid Discretizations

A number of new local and parallel discretization and adaptive nite element algorithms are proposed and analyzed in this paper for elliptic boundary value problems. These algorithms are motivated by the observation that, for a solution to some elliptic problems, low frequencycomponents can be approximated well by a relatively coarse grid and high frequency components can be computed on a ne grid by some local and parallel procedure. The theoretical tools for analyzing these methods are some local a priori and a posteriori estimates that are also obtained in this paper for nite element solutions on general shape-regular grids. Some numerical experiments are also presented to support the theory.