Unconditional Stability and Error Estimates of the Modified Characteristics FEM for the Time-Dependent Viscoelastic Oldroyd Flows (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.