Michael J. Neilan

Michael J. Neilan is a Professor and Director of Graduate Studies in the Department of Mathematics at the University of Pittsburgh, part of the Dietrich School of Arts and Sciences. His research focuses on computational and applied mathematics, with emphasis on the finite element method, numerical approximations for nonlinear PDEs, and structure-preserving discretizations for incompressible fluid models and surface PDEs.

Education:

• PhD in Mathematics, University of Tennessee, 2009

Research Interests: Computational PDEs, finite element methods, structure-preserving discretizations, incompressible fluid dynamics, surface PDEs, fully nonlinear PDEs (e.g., Monge-Ampère equations, optimal transport), and discontinuous Galerkin methods.

Publications Trends: His work bridges theoretical analysis and computational implementation, with key contributions to mixed finite element methods, divergence-free formulations, and numerical techniques for nonlinear PDEs. Recent focus includes Monge-Ampère equations and stability analyses for fluid flow models.

Editorial Roles:

• Managing Editor, Mathematics of Computation
• Associate Editor, IMA Journal of Numerical Analysis
• Associate Editor, Calcolo
• Associate Editor, Journal of Numerical Mathematics

Professional Activities: Co-organizer of the Finite Element Circus, a leading conference in finite element theory and applications.