A note on fitted operator methods for a laminar jet problem

We consider the classical problem of a two-dimensional laminar jet of incompressible fluid flowing into a stationary medium of the same fluid [H. Schlichting, Boundary-Layer Theory, McGraw-Hill, 1979]. The equations of motion are the same as the boundary layer equations for flow over an infinite flat plate, but with different boundary conditions. It has been shown [A.R. Ansari et al., Parameter robust numerical solutions for the laminar free jet, submitted] that using an appropriate piecewise uniform mesh, numerical solutions together with their scaled discrete derivatives are obtained which are parameter (i.e., viscosity ν) robust with respect to both the number of mesh nodes and the number of iterations required for convergence. We prove that there do not exist fitted operator schemes which converge ν-uniformly if the fitting coefficients are independent of the problem data.