(untitled) (Advances in Applied Mathematics and Mechanics, 2020)
In this paper, our purpose is to study the unconditional stability and convergence of characteristics finite element method (FEM) for the time-dependent viscoelastic Oldroyd fluids motion equations. We deduce optimal error estimates in L^2 and H^1 norm. The analysis is based on an iterated time-discrete system, with which the error function is split into a temporal error and a spatial error. Finally, numerical results confirm the theoretical predictions.