Two types of spurious oscillations at layers diminishing methods for convection–diffusion–reaction equations on surface

Abstract

In this article, we consider the steady convection–diffusion–reaction equation posed on general surface in convection-dominated regimes, which is an important problem in many models for simulating substances transport on ultrathin material and solid surfaces. Two types of spurious oscillations at layers diminishing (SOLD) methods are considered when the streamline diffusion method cannot completely eliminates the spurious oscillations at layers for convection-dominated problem with nonsmooth solution. One is the edge stabilization method that uses least square stabilization of the gradient jumps a across element boundaries, the other, a Petrov–Galerkin method, is called the Mizukami–Hughes method. An error analysis of the edge stabilization method on surface is provided. Finally, numerical experiments including the comparisons among these methods are presented to illustrate the accuracy and efficiency of the SOLD methods.