The axisymmetric Poiseuille flow of a Johnson-Segalman fluid is selected as a specific one-dimensional example for testing numerical algorithms, while analytical results are also made available. A particular emphasis is put on the appearance of limit points with some numerical algorithms.
Van Schaftingen, J. J., & Crochet, M. (1985). Analytical and numerical solution of the Poiseuille flow of a Johnson-Segalman fluid. Journal of Non-Newtonian Fluid Mechanics, 18(3), 335-351. https://doi.org/10.1016/0377-0257(85)87006-3 (Original work published 1985)