<p>We study an iterative nonlinear solver for the Oldroyd-B system describing incompressible viscoelastic fluid flow. We establish a range of attributes of the fixed-point-based solver, together with the conditions under which it becomes contractive, and examine the smoothness properties of its corresponding fixed-point function. Under these properties, we demonstrate that the solver meets the necessary conditions for the recent Anderson acceleration (AA) framework, thereby showing that AA enhances the solver’s linear convergence rate. Results from three benchmark tests illustrate how AA improves the solver’s ability to converge as the Weissenberg number is increased.</p>