  The third-order Jeffery-Hamel ODE governing the flow of an incompressible
fluid in a two-dimensional wedge is briefly derived, and a C^1 finite element
formulation of the equation is developed. This formulation has several
advantages, including a natural framework for enforcing the boundary
conditions, a numerically efficient solution procedure, and suitability for
implementation within well-established, open, scientific computing tools. The
finite element formulation is shown to be non-coercive, and therefore not ideal
for proving existence, uniqueness, or a priori error estimates, but the
numerical solutions computed with quartic Hermite elements are nevertheless
found to converge to reference solutions at nearly optimal rates (O(h^4) in
both L^2 and H^1 norms). Further work is required to better understand the
cause of the suboptimal convergence rates, and a linear model problem which
exhibits analogous characteristics is also discussed as a possible starting
point for future theoretical analyses.
