Education and outreach
Douglas N. Arnold

Over the years I have greatly enjoyed the challenges and rewards of teaching from the beginning undergraduate to advanced graduate levels, and also of conveying the excitement and relevance of mathematics beyond the confines of academia to the interested public. A major project of mine during the years 1992 to 1994 was the introduction of high level computer graphics into the first year calculus classroom. When the Web came into being I transferred some of these to a Graphics for the Calculus Classroom web page, which was, at one point, listed as one of the 60 most frequently linked pages in the mathematical sciences. In spring 1997, I developed some Graphics for Complex Analysis as well. In 1996 I was also honored to receive the George W. Atherton Award for Excellence in Teaching, Penn State's highest level of recognition for undergraduate education.

Public outreach

I have given public lectures in various venues on various mathematical topics. A lecture I gave on the mathematics of golf can be seen here. My family has also endowed an annual public lecture held at the IMA.

Course materials

Some of my course materials are available on the web. As a motivator for numerical analysis students I have collected some examples of real life disasters resulting from bad numerics. I have extensive lecture notes on complex analysis and functional analysis at the level of a first year graduate course. Other materials is linked from various course home pages:

Ph.D. students

University of Maryland

My first Ph.D. student, Raymond Cheng received his degree in 1987 with a thesis entitled Delta-Trigonometric and Spline-Trigonometric Methods using the Single-Layer Potential Representation. Ray went on to become a research team leader in the Computational Mechanics Division of the Navy's David Taylor Model Basin and is now retired.

Patrick Noon received his Ph.D. in 1988. His thesis was entitled The Single Layer Heat Potential and Galerkin Boundary Element Methods for the Heat Equation. Pat is a Senior Software Engineer.

Penn State University

Xiaobo Liu received his degree in 1993. Xiaobo wrote his thesis on Interior Estimates for Some Nonconforming and Mixed Finite Element Methods. He is now a Managing Director at Wells Fargo.

Jason Qin completed his degree in 1994 with a thesis On the Convergence of Some Low Order Mixed Finite Elements for Incompressible Fluids. He is currently Chief Architect at AOL.

Changyi Chen graduated in 1995 with a thesis entitled Asymptotic convergence rates for the Kirchhoff plate model. He is currently on the faculty at College of Lake County.

Arup Mukherjee completed Ph.D. in 1996 with a thesis entitled An Adaptive Finite Element Code for Elliptic Boundary Value Problems in three dimensions with applications in Numerical Relativity. Arup is now an associate professor at Montclair State University.

Alexandre Madureira completed his Ph.D. in 1999 with a thesis entitled Asymptotics and Hierarchical Modeling of Thin Domains. He is a senior researcher at the Laboratório Nacional de Computaçio Científica (LNCC) in Brazil, where he has also served as chair of the Department of Applied and Computational Mathematics.

Sheng Zhang completed his Ph.D. in 2001. In his thesis, which is entitled A Linear Shell Theory Based on Variational Principles, he studied a variational approach to the derivation of dimensionally reduced models for elastic shells and obtains rigorous convergence estimates and rates for them. Sheng is associate professor at Wayne State University.

University of Minnesota

Nicolae Tarfulea completed his Ph.D. in 2004. In his thesis entitled Constraint Preserving Boundary Conditions for Hyperbolic Formulations of Einstein's Equations, he studied well-posed boundary conditions which preserve given differential constraints for first order symmetric hyperbolic evolutions relevant to Einstein's equations in a 3+1 formulation. Tarfulea is full professor at Purdue University Northwest.

Jeonghun (John) Lee completed his Ph.D. in 2012 at the University of Minnesota with a thesis entitled Mixed methods with weak symmetry for time dependent problems of elasticity and viscoelasticity. After postdoctoral appointments at Aalto University in Helsinki, University of Oslo, and University of Texas, John joined the faculty of Baylor University as an assistant professor in 2018.

Vincent Quenneville-Bélair completed his Ph.D. in 2015 at the University of Minnesota with a thesis entitled A new approach to finite element simulations of general relativity. Vincent's first position was as Chu Assistant Professor of Applied Mathematics at Columbia University. He currently is a machine learning scientist at Facebook.

Paula Dassbach completed her Ph.D. in 2017, under the joint supervision of M.C. Calderer and me, at the University of Minnesota with a thesis entitled Computational aspects of energy minimization of the Landau-de Gennes energy for liquid crystals and now works as a senior scientist at Medtronic.

Lizao Li completed his Ph.D. in 2018 at the University of Minnesota with a thesis entitled Regge finite elements with applications in solid mechanics and relativity. He now works as a research software engineer at Google.

Bo Yang completed his Ph.D. in 2019 at the University of Minnesota with a thesis entitled Robin boundary conditions for the Hodge Laplacian and Maxwell's equations. He now works as a software engineer at Microsoft.

Tyson Loudon completed his Ph.D. in 2021 at the University of Minnesota with a thesis entitled Lanczos approximation of joint spectral quantities and applications. He in now a Computational Mechanics and Dynamics Researcher for Survice Engineering.


Marie E. Rognes obtained her Ph.D. in 2008 from the University of Oslo where her primary advisor was Ragnar Winther. A portion of her thesis Mixed finite element methods with applications to viscoelasticity and gels, was written with me at the University of Minnesota during 2007-2008. Rognes is currently chief research scientist at Simula Research Laboratory.

Hongtao Chen obtained his Ph.D. in 2011 from the Chinese Academy of Sciences where his primary advisor was Lin Qun. His thesis was based on work carried out during 2010-2011 under my direction at University of Minnesota. Chen is now aa full professor at Xiamen University.

Martin Licht obtained his Ph.D. in 2017 from the University of Oslo where his primary advisor was Snorre Christiansen. A significant portion of his thesis, On the a priori and a posteriori error analysis in finite element exterior calculus, was developed during a visit I hosted at University of Minnesota during the 2015-2016 academic year. Martin is now a postdoc at EPFL in Lausanne, Switzerland.

Updated April 20, 2021