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.

本文在研究全离散标准有限元法的基础上，提出了一种求解扩散彼得林粘弹性模型的全离散二网格有限元法。全离散二元网格法涉及求解具有相同时间步长的小型非线性粗空间网格系统和线性细空间网格系统。在合理的假设下，理论上证明了在精细空间网格上，全离散二格法的精度与全离散有限元法的精度相同。通过数值算例验证了标准有限元法和二网格法的精度和收敛顺序。