We consider the application of least-squares variational principles to the numerical solution
of partial differential equations. Our main focus is on the development of least-squares finite …

This paper develops and analyzes two least-squares methods for the numerical solution of
linear, stationary incompressible Newtonian fluid flow in two and three dimensions. Both …

In this paper we study finite element methods of least-squares type for the stationary,
incompressible Navier--Stokes equations in two and three dimensions. We consider …

Least-squares finite element methods have become increasingly popular for the
approximate solution of first-order systems of partial differential equations. Here, after a brief …

We establish an a-posteriori error estimate, with corresponding bounds, that is valid for any
FOSLS L2-minimization problem. Such estimates follow almost immediately from the FOSLS …

Since their emergence in the early 1950s, finite element methods have become one of the
most versatile and powerful methodologies for the approximate numerical solution of partial …

The L 2-norm version of first-order system least squares (FOSLS) attempts to reformulate a
given system of partial differential equations so that applying a least-squares principle yields …

This paper develops two first-order system least-squares (FOSLS) approaches for the
solution of the pure traction problem in planar linear elasticity. Both are two-stage algorithms …

This paper continues the development of the least-squares methodology for the solution of
the incompressible Navier--Stokes equations started in Part I. Here we again use a velocity …

We compare three least-squares finite element reformulations of the Stokes equations,
paying particular attention to mass conservation. The first problem we approximate has a …