Department of Mathematics

Designing efficient and accurate numerical methods for partial differential equations arising in multiscale and multiphysics problems is a complicated process, involving a combination of analysis of simplified model problems, non-rigorous asymptotic analysis (a.k.a. "physical reasoning") and numerical experiments. We will show how these elements come together in various ways in several examples taken from current research, including methods for classical PDE in complex geometries, for low Mach number flow, and for problems with constraints.