Math Colloquium — Finite element methods for problems in electromagnetics

Speaker: Casey Cavanaugh, Colby College

Many problems in physics and engineering are governed by laws involving partial differential equations. In application, it is extremely difficult or impossible to generate analytical solutions, making the design and analysis of numerical methods essential. Numerical methods give approximate solutions and there are many questions to consider when thinking about what a “good” method is and what it means to be a “good” numerical solution. Are the theoretical properties of the continuous problem preserved on the discrete level? Does the numerical solution satisfy the underlying physical laws? Does the method converge, and if so, how quickly? In this talk, we will focus on PDEs arising from applications in electromagnetics problems (Maxwell’s equations), and explore some answers to these questions using mixed finite element methods.