The upper-convected Maxwell model of an elastic liquid is solved by means of the finite element method, using a penalty function approach. It is shown that the algorithm produces oscillations in the stresses in the presence of geometrical discontinuities, for increasing Deborah number De. The cause of this problem is explored and an indication of how to solve this problem is given. The complete set of equations appears to be of the mixed hyperbolic-elliptic type.
Zanden, van der, J. P. P. M., Kuiken, G. D. C., Segal, A., Lindhout, W. J., & Hulsen, M. A. (1985). Numerical experiments and theoretical analysis of the flow of an elastic liquid of the upper-convected Maxwell-Oldroyd type in the presence of geometrical discontinuities. Applied Scientific Research, 42(4), 303-318. https://doi.org/10.1007/BF00384209