A sparse finite element method with high accuracy Part I

In this paper, we develop and analyze a new finite element method called th e sparse finite element method for second order elliptic problems. This met hod involves much fewer degrees of freedom than the standard finite element method. We show nevertheless that such a sparse finite element method stil l possesses the superconvergence and other high accuracy properties same as those of the standard finite element method. The main technique in our ana lysis is the use of some integral identities.