Local and parallel finite element algorithms based on two-grid discretizations

A number of new local acid parallel discretization and adaptive finite elem ent algorithms are proposed and analyzed in this paper for elliptic boundar y value problems. These algorithms are motivated by the observation that, f or a solution to some elliptic problems, low frequency components can be ap proximated well by a relatively coarse grid and high frequency components c an be computed on a fine grid by some local and parallel procedure. The the oretical tools for analyzing these methods are some local a priori and a po steriori estimates that are also obtained in this paper for finite element solutions on general shape-regular grids. Some numerical experiments are al so presented to support the theory.