Convergence Analysis Of Nonconforming Finite Element Method For Bacterial Model

In this paper,Nonconforming finite element method is considered for a system of reaction-diffusion equations of bacterial infection with initial and boundary conditions under anisotropic meshes.Based on some special properties of the element and approaches for estimating the consistency error,the convergence analysis is presented and error estimates are derived under anisotropic meshes.The error estimates between numerical solutions and exact solutions are studied on the semi-discrete and the fully discrete finite element schemes,respectively.The optimal L~2 error estimates and H~1 superclose properties are derived.