L 2 error estimates for finite elements with interpolated boundary conditions

Summary TheL² error in the nearly zero quadratic approximate solution to Poisson's equation is shown to be of optimal order. The same method of proof can be used to show that theL² error with a space of cubics developed by Ridgway Scott is optimal.This work was supported by the Office of Naval Research under Contract Number ONR NR-044-453 and by the Naval Ordnance Laboratory Independent Research Fund.