Stable Numerical Methods for Viscoelastic Giesekus Model

This paper addresses the challenges of numerically solving the Giesekus model, a complex system used to model viscoelastic fluids. The authors focus on developing stable and convergent numerical methods, a significant improvement over existing methods that often suffer from accuracy and convergence issues. The paper's contribution lies in proving the convergence of the proposed method to a weak solution in two dimensions without relying on regularization, and providing an alternative proof of a recent existence result. This is important because it provides a reliable way to simulate these complex fluid behaviors.