We consider the classical problem of a two-dimensional laminar jet of incompressible fluid flowing into a stationary medium of the same fluid. The equations of motion are the same as the boundary layer equations for flow past an infinite flat plate, but with different boundary conditions. Numerical experiments show that, using appropriate piecewise-uniform meshes, numerical solutions together with their scaled discrete derivatives are obtained which are parameter (i.e., viscosity v) robust with respect to both the number of mesh nodes and the number of iterations required for convergence. While the method employed is non-conservative, we show with the aid of numerical experiments that the loss in conservation of momentum is minimal. Copyright (C) 2003 John Wiley Sons, Ltd.