A Finite Element Method for the Advection-Diffusion Equation
Recent increases in computing power have changed the way we are able to solve PDEs. One of the more popular ways to computationally solve differential equations is the finite element method (FEM). The objective of this project is to solve the 1-D advection-diffusion equation using this method in C++. For flows that are diffusion-dominated, the standard FEM approach can be used. However, advection-dominated flows result in physically unrealistic solutions. Therefore, we have to consider methods which preserve positivity, such as flux corrected transport. We will present numerical results for diffusion-dominated and purely advection-driven flow.