On the accuracy of least squares methods in the presence of corner singularities

This paper treats elliptic problems with corner singularities. Finite element approximations based on variational principles of the least squares type tend to display poor convergence properties in such contexts. Moreover, mesh refinement or the use of special singular elements do not appreciably improve matters. Here we show that if the least squares formulation is done in appropriately weighted spaces, then optimal convergence results in unweighted spaces like L².