The author considers \(\Delta u+2\sigma y^{-1}u_ y=f\) \((\sigma >0)\) on \(\Omega\), \(u=0\) on \(\Gamma\), \(u_ y=0\) on \(\Gamma_ 0\), where \(\Omega\) is a bounded convex domain in the upper half-plane, \(\partial \Omega\) intersects the x-axis in \(\Gamma_ 0\) and \(\Gamma_ 1\) is the rest of \(\partial \Omega\). The author uses the symmetric bilinear form \((y^{2\sigma}\nabla u,\nabla \phi)\) and for \(\sigma >1/2\) a nonsymmetric form with principle part (y \(\nabla u,\nabla \phi)\). \(\Gamma_ 1\) is assumed to be polygonal and to meet \(\Gamma_ 0\) at right angles. For a finite element approximation on a mesh of size h the author proves that in both formulations the solution is a best approximation in a weighted \(H^ 1\) seminorm, that convergence is optimal in a weighted \(L^ 2\) norm, and that in the symmetric formulation is ``almost best'' in \(L^{\infty}\). Numerical results indicate that the nonsymmetric formulation gives smaller errors.