Advection-diffusion

Abstract

In this chapter, we want to solve a model problem where the PDE comprises a first-order differential operator modeling advection processes and a second-order term modeling diffusion processes. The difficulty in approximating an advection-diffusion equation can be quantified by the Péclet number which is equal to the meshsize times the advection velocity divided by the diffusion coefficient. When the Péclet number is large, the standard Galerkin approximation is plagued by spurious oscillations. These oscillations disappear if very fine meshes are used, but a more effective approach using coarser meshes is to resort to stabilization. In this chapter, we focus on the Galerkin/least-squares (GaLS) stabilization, but any stabilized $H^1$-conforming method or the dG method can also be used.