A staggered discontinuous Galerkin method for the convection–diffusion equation

This paper is concerned with the staggered discontinuous Galerkin metho d for convection–diffusion equations. Over the past few decades, stagger ed type methods have been applied successfully to many problems, such as wave propagation and fl uid flow problems. A distinctive feature of these methods is that the physical laws arising from th e corresponding partial differential equations are automatically preserved. Nevertheles s, staggered methods for convection–diffusion equations are rarely seen in literature. It is thus the main goal of this paper to develop and analyze a class of staggered numerical schemes for the approximation of convection–diffusion equations. We will prove that our new method pres erv the underlying physical laws in some discrete sense. Moreover, the stability and conver gence of the method are proved. Numerical results are shown to verify the theoretical estimates.