A new combined scheme of H~1-Galerkin FEM and TGM for bacterial equations

摘要

In this paper, a new combined second order fully discrete scheme of an H~1-Galerkin finite element method (H~1-GFEM) with two grid method (TGM) is developed for the bacterial equations. Based on Q_(11)/Q_(1.0) × Q_(0.1) element pair, the existence and uniqueness of the approximation solution are proved, and the superclose and superconvergent estimates of order O(h~2 4- H~4 + τ~2) for the original variables in H~1-norm and intermediate variables in L~2-norm are derived, respectively. Some numerical results are provided to show that the proposed method has a very good performance and its computing cost is only about half of H~1-GFEM for the considered problem. Here, the sizes of coarse mesh, fine mesh and time step are denoted by H, h, τ, respectively.