A new two-grid nonconforming mixed finite element method for nonlinear Benjamin-Bona-Mahoney equation

摘要

A new low order two-grid mixed finite element method (FEM) is developed for the nonlinear Benjamin-Bona-Mahoney (BBM) equation, in which the famous nonconforming rectangular CNQ1rot element and Q0 × Q0 constant element are used to approximate the exact solution u and the variable p→=∇ut, respectively. Then, based on the special properties of these two elements and interpolation post-processing technique, the superconvergence results for u in broken H1-norm and p→ in L2-norm are obtained for the semi-discrete and Crank-Nicolson fully-discrete schemes without the restriction between the time step τ and coarse mesh size H or the fine mesh size h, which improve the results of the existing literature. Finally, some numerical results are provided to confirm the theoretical analysis.