  This paper studies adaptive least-squares finite element methods for
convection-dominated diffusion-reaction problems. The least-squares methods are
based on the first-order system of the primal and dual variables with various
ways of imposing outflow boundary conditions. The coercivity of the homogeneous
least-squares functionals are established, and the a priori error estimates of
the least-squares methods are obtained in a norm that incorporates the
streamline derivative. All methods have the same convergence rate provided that
meshes in the layer regions are fine enough. To increase computational accuracy
and reduce computational cost, adaptive least-squares methods are implemented
and numerical results are presented for some test problems.
