Analysis and Simulation of an Improved Fast Two‐Grid Mixed Element Method for a Nonlinear Time Fractional Pseudo‐Hyperbolic Equation

ABSTRACT In this article, an improved fast two‐grid mixed element algorithm is developed for a nonlinear time fractional pseudo‐hyperbolic wave equation model. By introducing two auxiliary variables, the original problem is transformed into a lower‐order coupled system with three equations, and then a fully discrete nonlinear mixed element system is formulated, where the spatial direction is approximated by the provided mixed element method, and the temporal direction is discretized using the approximation. To further address the computational time issue caused by nonlinear iterations, a fast two‐grid mixed finite element algorithm in space is constructed. The stability and error estimates for the fully discrete improved fast two‐grid mixed element algorithm are derived. Finally, by the comparison with the computing results of the nonlinear mixed element algorithm, it is evident that the proposed two‐grid mixed finite element algorithm significantly improves computational efficiency.