A fully discrete two-grid method for the diffusive Peterlin viscoelastic model

We present in this paper a fully discrete two-grid finite element method to solve the diffusive Peterlin viscoelastic model on the basis of studying the fully discrete standard finite element method. The fully discrete two-grid method involves solving small nonlinear coarse spatial grid systems and linear fine spatial grid systems with the same time step. Under the reasonable assumptions, it is proven theoretically that the accuracy of fully discrete two-grid method is the same as the fully discrete finite element method on the fine spatial grid. Numerical examples are given to validate the accuracy and convergence order of the standard finite element method and two-grid method.