New Discontinuous Galerkin Finite Element Methods On Overlapping Cells In 2D

In the past twenty years, the discontinuous galerkin finite element method is widely used in aerodynamics, plasma physics, semiconductor and other fields. By the development of the method, some new discontinuous galerkin methods have been proposed. In this paper, we will discuss the discontinuous galerkin method and the central discontinuous galerkin method on overlapping cells and apply them to problems in 2D. The numerical results showed that:for conservation law, the convergence rate of the discontinuous galerkin method and the central discontinuous Galerkin method are k+1; for diffusion equation, the convergence rate of the discontinuous galerkin method is k if k= 1, it's k+1 if k≠1, the convergence rate of the central discontinuous galerkin method on overlapping cells is k+1 in both cases.