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 H1-norm and the Hdiv-norm, but also in the L2-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.