@unpublished{AwFaGuSt2020, author = {Gerard Awanou and Maurice Fabien and Johnny Guzm\'an and Ari Stern}, eprint = {2008.00149}, note = {preprint}, primaryclass = {math.NA}, title = {Hybridization and postprocessing in finite element exterior calculus}, year = {2020} }

@article{BeSt2020a, author = {Yakov Berchenko-Kogan and Ari Stern}, eprint = {1907.00084}, fjournal = {Foundations of Computational Mathematics}, journal = {Found. Comput. Math.}, note = {in press}, primaryclass = {math.NA}, title = {Constraint-preserving hybrid finite element methods for {M}axwell's equations}, year = {2020} }

@unpublished{BeSt2020b, author = {Yakov Berchenko-Kogan and Ari Stern}, eprint = {2003.10054}, note = {preprint}, primaryclass = {math.NA}, title = {Charge-conserving hybrid methods for the {Y}ang--{M}ills equations}, year = {2020} }

@article{BrGoFrMcStChOwAlSuHaCaHoFaMoBeAn2016, author = {Brier, Matthew R. and Gordon, Brian and Friedrichsen, Karl and McCarthy, John and Stern, Ari and Christensen, Jon and Owen, Christopher and Aldea, Patricia and Su, Yi and Hassenstab, Jason and Cairns, Nigel J. and Holtzman, David M. and Fagan, Anne M. and Morris, John C. and Benzinger, Tammie L. S. and Ances, Beau M.}, doi = {10.1126/scitranslmed.aaf2362}, issn = {1946-6234}, journal = {Science Translational Medicine}, number = {338}, pages = {338ra66}, publisher = {American Association for the Advancement of Science}, title = {Tau and {A$\beta$} imaging, {CSF} measures, and cognition in {A}lzheimer's disease}, volume = {8}, year = {2016} }

@article{BrMcBeStSuFrMoAnVl2016, author = {Brier, Matthew R. and McCarthy, John E. and Benzinger, Tammie L. S. and Stern, Ari and Su, Yi and Friedrichsen, Karl A. and Morris, John C. and Ances, Beau M. and Vlassenko, Andrei G.}, doi = {10.1016/j.neurobiolaging.2015.10.025}, fjournal = {Neurobiology of Aging}, journal = {Neurobiol. Aging}, pages = {104--111}, title = {Local and distributed {PiB} accumulation associated with development of preclinical {Alzheimer's} disease}, volume = {38}, year = {2016} }

@article{ChRaSt2020, author = {Zhengdao Chen and Baranidharan Raman and Ari Stern}, doi = {10.1137/18M123390X}, eprint = {1811.00173}, fjournal = {SIAM Journal on Scientific Computing}, journal = {SIAM J. Sci. Comput.}, number = {1}, pages = {B273--B298}, primaryclass = {math.NA}, title = {Structure-preserving numerical integrators for {H}odgkin--{H}uxley-type systems}, volume = {42}, year = {2020} }

@article{HoSt2012a, author = {Michael Holst and Ari Stern}, doi = {10.1007/s10208-012-9119-7}, eprint = {1005.4455}, fjournal = {Foundations of Computational Mathematics}, journal = {Found. Comput. Math.}, number = {3}, pages = {263--293}, primaryclass = {math.NA}, title = {Geometric variational crimes: {H}ilbert complexes, finite element exterior calculus, and problems on hypersurfaces}, volume = {12}, year = {2012} }

@article{HoSt2012b, author = {Michael Holst and Ari Stern}, doi = {10.1007/s10208-011-9110-8}, eprint = {1010.6127}, fjournal = {Foundations of Computational Mathematics}, journal = {Found. Comput. Math.}, number = {3}, pages = {363--387}, primaryclass = {math.NA}, title = {Semilinear mixed problems on {H}ilbert complexes and their numerical approximation}, volume = {12}, year = {2012} }

@article{LeSt2016, author = {Paul Leopardi and Ari Stern}, doi = {10.1137/15M1047684}, eprint = {1401.1576}, fjournal = {SIAM Journal on Numerical Analysis}, journal = {SIAM J. Numer. Anal.}, number = {6}, primaryclass = {math.NA}, title = {The abstract {H}odge--{D}irac operator and its stable discretization}, volume = {54}, year = {2016} }

@article{LiStTa2017, author = {Li, Songhao and Stern, Ari and Tang, Xiang}, doi = {10.3842/SIGMA.2017.019}, eprint = {1511.00061}, fjournal = {SIGMA. Symmetry, Integrability and Geometry. Methods and Applications}, issn = {1815-0659}, journal = {SIGMA Symmetry Integrability Geom. Methods Appl.}, pages = {019, 26 pages}, primaryclass = {math.DS}, title = {Lagrangian mechanics and reduction on fibered manifolds}, volume = {13}, year = {2017} }

@article{MaMaSt2015, author = {Marrero, Juan Carlos and Mart\'in de Diego, David and Stern, Ari}, doi = {10.3934/dcds.2015.35.367}, eprint = {1103.6250}, fjournal = {Discrete and Continuous Dynamical Systems. Series A}, journal = {Discrete Contin. Dyn. Syst.}, number = {1}, pages = {367--397}, primaryclass = {math.SG}, title = {Symplectic groupoids and discrete constrained {L}agrangian mechanics}, volume = {35}, year = {2015} }

@article{McSt2014, author = {Robert I. McLachlan and Ari Stern}, doi = {10.1137/130921118}, eprint = {1305.3216}, fjournal = {SIAM Journal on Numerical Analysis}, journal = {SIAM J. Numer. Anal.}, number = {3}, pages = {1378--1397}, primaryclass = {math.NA}, title = {Modified trigonometric integrators}, volume = {52}, year = {2014} }

@article{McSt2020, author = {Robert I. McLachlan and Ari Stern}, doi = {10.1007/s10208-019-09415-1}, eprint = {1705.08609}, fjournal = {Foundations of Computational Mathematics}, journal = {Found. Comput. Math.}, number = {1}, pages = {35--69}, primaryclass = {math.NA}, title = {Multisymplecticity of hybridizable discontinuous {G}alerkin methods}, volume = {20}, year = {2020} }

@unpublished{MiSt2015, author = {Evan Miller and Ari Stern}, eprint = {1507.05030}, note = {preprint}, primaryclass = {math.AP}, title = {Maximum principles for the relativistic heat equation}, year = {2015} }

@article{MuStVe2020, author = {Hans Z. Munthe-Kaas and Ari Stern and Olivier Verdier}, doi = {10.1137/19M1252879}, eprint = {1903.10056}, fjournal = {SIAM Journal on Applied Algebra and Geometry}, journal = {SIAM J. Appl. Algebra Geom.}, number = {1}, pages = {49--68}, primaryclass = {math.DG}, title = {Invariant connections, {L}ie algebra actions, and foundations of numerical integration on manifolds}, volume = {4}, year = {2020} }

@article{NoMcQuStZa2015, author = {Richard A. Norton and David I. McLaren and G. Reinout W. Quispel and Ari Stern and Antonella Zanna}, doi = {10.3934/dcds.2015.35.2079}, eprint = {1302.2713}, fjournal = {Discrete and Continuous Dynamical Systems. Series A}, journal = {Discrete Contin. Dyn. Syst.}, number = {5}, pages = {2079--2098}, primaryclass = {math.NA}, title = {Projection methods and discrete gradient methods for preserving first integrals of {ODE}s}, volume = {35}, year = {2015} }

@unpublished{OlSt2020, author = {Peter J. Olver and Ari Stern}, eprint = {2005.12260}, note = {preprint}, primaryclass = {nlin.PS}, title = {Dispersive fractalization in linear and nonlinear {F}ermi--{P}asta--{U}lam--{T}singou lattices}, year = {2020} }

@unpublished{SmStTrZh2017, author = {Graham Smith and Ari Stern and Hung Tran and Detang Zhou}, eprint = {1709.00977}, note = {preprint}, primaryclass = {math.DG}, title = {On the {M}orse index of higher-dimensional free boundary minimal catenoids}, year = {2017} }

@phdthesis{Stern2009, author = {Ari Stern}, school = {California Institute of Technology}, title = {Geometric discretization of {L}agrangian mechanics and field theories}, url = {http://resolver.caltech.edu/CaltechETD:etd-12312008-173851}, year = {2009} }

@article{Stern2010, author = {Ari Stern}, doi = {10.4310/JSG.2010.v8.n2.a5}, eprint = {0905.4318}, fjournal = {The Journal of Symplectic Geometry}, journal = {J. Symplectic Geom.}, number = {2}, pages = {225--238}, primaryclass = {math.SG}, title = {Discrete {H}amilton--{P}ontryagin mechanics and generating functions on {L}ie groupoids}, volume = {8}, year = {2010} }

@article{Stern2013, author = {Ari Stern}, doi = {10.7153/mia-16-04}, eprint = {1004.0401}, fjournal = {Mathematical Inequalities \& Applications}, journal = {Math. Inequal. Appl.}, number = {1}, pages = {55--67}, primaryclass = {math.DG}, title = {{$L^p$} change of variables inequalities on manifolds}, volume = {16}, year = {2013} }

@article{Stern2015, author = {Ari Stern}, doi = {10.1007/s00211-014-0658-5}, eprint = {1307.4393}, fjournal = {Numerische Mathematik}, journal = {Numer. Math.}, pages = {125--133}, primaryclass = {math.NA}, title = {Banach space projections and {P}etrov--{G}alerkin estimates}, volume = {130}, number = {1}, year = {2015} }

@inproceedings{StDe2006, address = {New York}, author = {Ari Stern and Mathieu Desbrun}, booktitle = {SIGGRAPH '06: ACM SIGGRAPH 2006 Courses}, doi = {10.1145/1185657.1185669}, isbn = {1-59593-364-6}, location = {Boston, Massachusetts}, pages = {75--80}, publisher = {ACM Press}, title = {Discrete geometric mechanics for variational time integrators}, year = {2006} }

@article{StGr2009, author = {Ari Stern and Eitan Grinspun}, doi = {10.1137/080732936}, eprint = {0808.2239}, fjournal = {Multiscale Modeling \& Simulation. A SIAM Interdisciplinary Journal}, journal = {Multiscale Model. Simul.}, number = {4}, pages = {1779--1794}, primaryclass = {math.NA}, title = {Implicit-explicit variational integration of highly oscillatory problems}, volume = {7}, year = {2009} }

@article{StTe2019, author = {Ari Stern and Alexander Tettenhorst}, doi = {10.1016/j.geb.2018.09.006}, eprint = {1709.08318}, fjournal = {Games and Economic Behavior}, issn = {0899-8256}, journal = {Games Econom. Behav.}, pages = {186--198}, primaryclass = {cs.GT}, title = {Hodge decomposition and the {S}hapley value of a cooperative game}, volume = {113}, year = {2019} }

@article{StToDeMa2008, author = {Ari Stern and Yiying Tong and Mathieu Desbrun and Jerrold E. Marsden}, doi = {10.2529/PIERS071019000855}, eprint = {0803.2070}, journal = {PIERS Online}, number = {7}, pages = {711--715}, primaryclass = {math.NA}, title = {Variational integrators for {M}axwell's equations with sources}, volume = {4}, year = {2008} }

@incollection{StToDeMa2015, address = {New York}, author = {Ari Stern and Yiying Tong and Mathieu Desbrun and Jerrold E. Marsden}, booktitle = {Geometry, mechanics, and dynamics}, doi = {10.1007/978-1-4939-2441-7_19}, editor = {Chang, Dong Eui and Holm, Darryl D. and Patrick, George and Ratiu, Tudor}, eprint = {0707.4470}, isbn = {978-1-4939-2440-0}, pages = {437-475}, primaryclass = {math.NA}, publisher = {Springer}, series = {Fields Institute Communications}, title = {Geometric computational electrodynamics with variational integrators and discrete differential forms}, volume = {73}, year = {2015} }

@article{WaFeYaSt2019, author = {Matthew Wallace and Renato Feres and Gregory Yablonsky and Ari Stern}, doi = {10.1016/j.compchemeng.2016.06.007}, eprint = {1511.02776}, fjournal = {Computers & Chemical Engineering}, journal = {Comput. Chem. Eng.}, pages = {612--622}, primaryclass = {cond-mat.soft}, title = {Explicit formulas for reaction probability in reaction-diffusion experiments}, volume = {125}, year = {2019} }