Ari Stern
Assistant Professor of Mathematics, Washington University in
St. Louis
About Me
I received my B.A. and M.A. from the mathematics department at
Columbia University. In 2009, I completed my Ph.D. in Applied
and Computational Mathematics at Caltech, under the direction of
the late
Jerrold
E. Marsden
and Mathieu
Desbrun. Before arriving at Wash. U. in 2012, I was a
postdoc in the mathematics department at UCSD, where I worked
with Michael
Holst.
Teaching (Spring 2015)
Math 131, Calculus
I.
Math 450, Numerical Methods for
Differential Equations.
Previous Courses
Fall 2014: Math 449, Numerical
Applied Mathematics.
Spring 2014: Math 515, Partial
Differential Equations.
Fall 2013: Math 456, Topics in
Financial Mathematics.
Spring 2013: Math 5052, Measure
Theory and Functional Analysis II.
Fall 2012: Math 5051, Measure
Theory and Functional Analysis I.
Research Interests
My research lies at the intersection of geometry, applied
analysis, and computational mathematics. I am interested in what I
call geometric numerical analysis: using geometry as a
means to develop novel numerical methods and techniques to analyze
them. The driving idea behind this work is the need for numerical
methods for differential equations that are
accurate globally, not just locally—and, in recent
years, it has been shown that these global features have important
(and often surprising) connections with modern geometry,
particularly differential and symplectic geometry.
Papers Available for Download


Norton, R. A., D. I. McLaren,
G. R. W. Quispel, A. Stern, and
A. Zanna (2015), Projection methods and discrete gradient
methods for preserving first integrals of ODEs. Discrete
Contin. Dyn. Syst., 35 (5), 20792098.
[ bib 
doi 
arXiv ]


Marrero, J. C., D. Martín de Diego, and
A. Stern (2015), Symplectic groupoids and discrete
constrained Lagrangian mechanics. Discrete
Contin. Dyn. Syst., 35 (1), 367397.
[ bib 
doi 
arXiv ]


Leopardi, P., and A. Stern (2014), The abstract
HodgeDirac operator and its stable discretization. Preprint.
[ bib 
arXiv ]


McLachlan, R. I., and A. Stern (2014), Modified
trigonometric integrators. SIAM
J. Numer. Anal., 52 (3), 13781397.
[ bib 
doi 
arXiv ]


Stern, A. (2014), Banach space projections and PetrovGalerkin
estimates. Numer. Math.
[ bib 
doi 
arXiv ]


Stern, A., Y. Tong, M. Desbrun, and
J. E. Marsden (2014), Geometric computational
electrodynamics with variational integrators and discrete
differential forms. Geometry, mechanics, and
dynamics: the legacy of Jerry Marsden, Fields
Inst. Commun., Springer. In press.
[ bib 
arXiv ]


Stern, A. (2013), L^{p} change of variables
inequalities on
manifolds. Math. Inequal. Appl., 16 (1), 5567.
[ bib 
doi 
arXiv ]


Holst, M., and A. Stern (2012), Semilinear mixed problems
on Hilbert complexes and their numerical
approximation. Found. Comput. Math., 12 (3),
363387.
[ bib 
doi 
arXiv ]


Holst, M., and A. Stern (2012), Geometric variational
crimes: Hilbert complexes, finite element exterior calculus,
and problems on
hypersurfaces. Found. Comput. Math., 12 (3),
263293.
[ bib 
doi 
arXiv ]


Stern, A. (2010), Discrete HamiltonPontryagin mechanics and
generating functions on Lie groupoids. J. Symplectic
Geom., 8 (2), 225238.
[ bib 
doi 
arXiv ]


Stern, A., and E. Grinspun (2009), Implicitexplicit
variational integration of highly oscillatory
problems. Multiscale Model. Simul., 7 (4),
17791794.
[ bib 
doi 
arXiv ]


Stern, A. (2009), Geometric discretization of Lagrangian
mechanics and field theories. Ph.D. thesis, California
Institute of Technology.
[ bib 
http ]


Stern, A., Y. Tong, M. Desbrun, and
J. E. Marsden (2008), Variational integrators for
Maxwell's equations with sources. PIERS Online,
4 (7), 711715.
[ bib 
doi 
arXiv ]


Stern, A., and M. Desbrun (2006), Discrete geometric
mechanics for variational time integrators. In SIGGRAPH
'06: ACM SIGGRAPH 2006 Courses, pages 7580, ACM Press,
New York.
[ bib 
doi ]
Contact
Ari Stern
Department of Mathematics
Washington University in St. Louis
Campus Box 1146
One Brookings Drive
St. Louis, MO 631304889
Email: astern@math.wustl.edu