On spurious oscillations at layers diminishing (SOLD) methods for convection–diffusion equations: Part I – A review

An unwelcome feature of the popular streamline upwind/Petrov–Galerkin (SUPG) stabilization of convection-dominated convection–diffusion equations is the presence of spurious oscillations at layers. Since the mid of the 1980s, a number of methods have been proposed to remove or, at least, to diminish these oscillations without leading to excessive smearing of the layers. The paper gives a review and state of the art of these methods, discusses their derivation, proposes some alternative choices of parameters in the methods and categorizes them. Some numerical studies which supplement this review provide a first insight into the advantages and drawbacks of the methods.