(untitled) (Advances in Applied Mathematics and Mechanics, 2018)
Nonconforming EQ^rot_1 element is applied to solving a kind of nonlinear Benjamin-Bona-Mahony (BBM for short) equation both for space-discrete and fully discrete schemes. A new important estimate is proved, which improves the result of previous works with the exact solution u belonging to H^2(Ω) instead of H^3(Ω). And then, the supercloseness and global superconvergence estimates in broken H^1 norm are obtained for space-discrete scheme. Further, the superclose estimates are deduced for backward Euler and Crank-Nicolson schemes. To confirm our theoretical analysis, numerical experiments for backward Euler scheme are executed. It seems that the results presented herein have never been seen for nonconforming FEMs in the existing literature.