Dr. Neilan's research interests include finite element methods and their convergence analysis for fully nonlinear partial differential equations. His current focus is on the construction and analysis of reliable and efficient numerical methods for the Monge-Ampere equation though the use of simple and practical finite elements. Other research interests of his include the numerical approximation of fluid flow (Stokes/Navier Stokes/Brinkman), the design and implementation of fourth and sixth order elliptic PDEs that arise in, e.g., plate bending and phase-field problems, the theory and construction of nonconforming finite element methods, and singular perturbation problems.