Eliminating the Gibbs phenomenon: the non-linear Petrov-Galerkin method for the convection-diffusion-reaction equation - Roggendorf, Sarah (2019)
In this thesis we consider the numerical approximation of the convection-diffusion-reaction equation. One of the main challenges of designing a numerical method for this problem is that boundary and interior layers typically present in the convection-dominated case can lead to non-physical oscillations in the numerical approximation, often referred to as Gibbs phenomena. The aim of this thesis is to develop a numerical method that eliminates Gibbs phenomena in the numerical approximation.