Two-grid mixed finite element method combined with the BDF2-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si371.svg" display="inline" id="d1e4182"><mml:mi>θ</mml:mi></mml:math> for a two-dimensional nonlinear fractional pseudo-hype

In this article, a fast two-grid mixed finite element (T-GMFE) algorithm based on a time second-order discrete scheme with parameter θ is considered to numerically solve a class of two-dimensional nonlinear fractional pseudo-hyperbolic wave models. The weighted and shifted Grünwald difference (WSGD) formula is used to approximate the fractional time derivative at time tn−θ, and the spatial direction is approximated by a two-grid H1-Galerkin MFE method. The error estimates in both L2 and H1-norm for the fully discrete T-GMFE system are proved. Further, a modified T-GMFE scheme is proposed and the optimal error results are provided. Finally, computing results show the presented T-GMFE method can save computing time and improve the computational efficiency.