Theses

Alex's doctoral thesis is concerned with the development of finite element methods for coupled systems of partial differential equations (PDEs) relating to problems in charge transport. The main focus is on structure-preserving approaches, which imitate at the discrete level properties possessed by the governing PDEs. This can include phenomena such as mass conservation, preserving the positivity of density variables, and energy decay laws. Aside from being desirable from a physical interpretation standpoint, structure-preserving methods can also benefit from inherent stability properties as a result of working within the natural framework of the problem.