  We propose a new first-order-system least squares (FOSLS) finite-element
discretization for singularly perturbed reaction-diffusion equations. Solutions
to such problems feature layer phenomena, and are ubiquitous in many areas of
applied mathematics and modelling. There is a long history of the development
of specialized numerical schemes for their accurate numerical approximation. We
follow a well-established practice of employing a priori layer-adapted meshes,
but with a novel finite-element method that yields a symmetric formulation
while also inducing a so-called "balanced" norm. We prove continuity and
coercivity of the FOSLS weak form, present a suitable piecewise uniform mesh,
and report on the results of numerical experiments that demonstrate the
accuracy and robustness of the method.
