Energy dissipative characteristic schemes for the diffusive Oldroyd-B viscoelastic fluid

In this paper, we propose new energy dissipative characteristic numerical methods for the approximation of diffusive Oldroyd-B equations that are based either on the finite element or finite difference discretization. We prove energy stability of both schemes and illustrate their behavior on a series of numerical experiments. Using both the diffusive model and the logarithmic transformation of the elastic stress, we are able to obtain methods that converge as mesh parameter is refined. Copyright (C) 2015 John Wiley & Sons, Ltd.