Superconvergence Analysis of Nonconforming Finite Element Method for BBM-Burgers Equation

The superconvergence behavior of the linearized BDF format with the nonconforming EQ^rot₁ element for the Benjamin-Bona-Mahony-Burgers (BBM-Burgers) equation was studied. By using mathematical induction to deal with the nonlinear term, together with the high accuracy analysis of this element and interpolation post-processing technique, then the superclose and superconvergence results of order O(h²+τ²) were derived in the broken H¹-norm without any restriction between the mesh size and time step. Finally, the correctness of the theoretical analysis was verified by a numerical example.