Error estimates for least squares finite element methods

A least squares finite element scheme for a boundary value problem associated with a second-order partial differential equation is considered. Previous work on this subject is generalized and improved by considering a larger class of equations, by working in the natural context, without additional smoothness conditions, and by deriving error estimates, not only in the H-1-norm and the H-div-norm, but also in the L-2-norm. Some of these estimates are sharpened by using finite element spaces with the grid decomposition property. The error estimates are supported by numerical results which extend previous numerical work. (C) 2002 Elsevier Science Ltd. All rights reserved.