2026 Douglas N. Arnold: Mathematics Researcher – H-Index, Publications & Awards

Discipline name	D-Index	World Ranking	Current World Ranking	National Ranking	Current National Ranking	Publications	Citations
Mathematics	57	666	566	333	264	114	22556
Engineering and Technology	56	2749	2629	832	756	108	22425

Research.com Recognitions

2013 - Fellow of the American Mathematical Society
2010 - Fellow of the American Association for the Advancement of Science (AAAS)
2009 - SIAM Fellow For contributions to finite elements and the numerical analysis of partial differential equations.
2008 - Fellow of John Simon Guggenheim Memorial Foundation

Overview

Douglas N. Arnold is affiliated with the University of Minnesota in the United States. Their primary research spans the fields of Engineering and Physics and Astronomy, focusing on several key subfields including Computational Theory and Mathematics, Computational Mechanics, Mathematical Physics, Atomic and Molecular Physics and Optics, and Mechanics of Materials.

Their work explores a range of advanced topics, notably:

Advanced Mathematical Modeling in Engineering
Advanced Numerical Methods in Computational Mathematics
Numerical methods in engineering
Spectral Theory in Mathematical Physics
Quantum chaos and dynamical systems
Random Matrices and Applications
Advanced Mathematical Physics Problems

Douglas N. Arnold has contributed to multiple scholarly publications. Key recent papers include:

"Local L²-bounded commuting projections in FEEC", 2021, ESAIM Mathematical Modelling and Numerical Analysis
"The Landscape Law for Tight Binding Hamiltonians", 2022, Communications in Mathematical Physics
"Complexes from Complexes", 2021, Foundations of Computational Mathematics
"Sharp estimates for the integrated density of states in Anderson tight-binding models", 2021, Physical Review A
"Spectral functions and localization-landscape theory in speckle potentials", 2022, Physical Review A

Publication venues frequently associated with their work include:

Physical Review A
arXiv (Cornell University)
ESAIM Mathematical Modelling and Numerical Analysis
Communications in Mathematical Physics
Foundations of Computational Mathematics

Their collaboration network includes frequent coauthors such as Marcel Filoche, Svitlana Mayboroda, Shiwen Zhang, Johnny Guzmán, and Wei Wang.

Douglas N. Arnold has been recognized within the academic community through several awards, including:

Fellow of the American Mathematical Society (2013)
Fellow of the American Association for the Advancement of Science (AAAS) (2010)
SIAM Fellow (2009) for contributions to finite elements and the numerical analysis of partial differential equations
Fellow of John Simon Guggenheim Memorial Foundation (2008)

Best Publications

Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems

Douglas N. Arnold;Franco Brezzi;Bernardo Cockburn;L. Donatella Marini

4323
Citations
An Interior Penalty Finite Element Method with Discontinuous Elements

Douglas N. Arnold

2141
Citations
A stable finite element for the stokes equations

D. N. Arnold;F. Brezzi;M. Fortin

1589
Citations
Finite element exterior calculus, homological techniques, and applications

Douglas N. Arnold;Richard S. Falk;Ragnar Winther

1214
Citations
Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates

D. N. Arnold;F. Brezzi

1198
Citations
Finite element exterior calculus: From hodge theory to numerical stability

Douglas N. Arnold;Richard S. Falk;Ragnar Winther

870
Citations
MATHEMATICAL ELASTICITY: VOLUME I: THREE-DIMENSIONAL ELASTICITY

Philippe G. Ciarlet

590
Citations
Multigrid in H(div) and H(curl)

Douglas N. Arnold;Richard S. Falk;Ragnar Winther

540
Citations
PEERS: A new mixed finite element for plane elasticity

Douglas N. Arnold;Franco Brezzi;Jim Douglas

533
Citations
Computer Solution of Ordinary Differential Equations.

Douglas N. Arnold;L. F. Shampine;M. K. Gordon

506
Citations
Mixed finite elements for elasticity

Douglas N. Arnold;Ragnar Winther

504
Citations
A uniformly accurate finite element method for the Reissner-Mindlin plate

D. N. Arnold;R. S. Falk

390
Citations
Mixed finite element methods for linear elasticity with weakly imposed symmetry

Douglas N. Arnold;Richard S. Falk;Ragnar Winther

366
Citations
Approximation by quadrilateral finite elements

Douglas N. Arnold;Daniele Boffi;Richard S. Falk

344
Citations
On the asymptotic convergence of collocation methods

Douglas N. Arnold;Wolfgang L. Wendland

340
Citations
Discontinuous Galerkin Methods for Elliptic Problems

Douglas N. Arnold;Franco Brezzi;Bernardo Cockburn;Donatella Marini

338
Citations
A family of higher order mixed finite element methods for plane elasticity

Douglas N. Arnold;Jim Douglas;Chaitan P. Gupta

331
Citations
Quadrilateral H (div) Finite Elements

Douglas N. Arnold;Daniele Boffi;Richard S. Falk

310
Citations
Locally Adapted Tetrahedral Meshes Using Bisection

Douglas N. Arnold;Arup Mukherjee;Luc Pouly

306
Citations
Preconditioning in H (div) and applications

Douglas N. Arnold;Richard S. Falk;R. Winther

289
Citations
Mixed finite element methods for elliptic problems

D. N. Arnold

264
Citations
Finite Element Exterior Calculus

Douglas N. Arnold

180
Citations
Multigrid inH(div) andH(curl )

Douglas N. Arnold;Richard S. Falk;Ragnar Winther

5
Citations

Frequent Co-Authors

Richard S. Falk Rutgers, The State University of New Jersey

Ragnar Winther University of Oslo

Franco Brezzi National Research Council (CNR)

Guy David University of Paris-Saclay

David Jerison MIT

Daniele Boffi King Abdullah University of Science and Technology

Wolfgang L. Wendland University of Stuttgart

Ivo Babuška The University of Texas at Austin

Bernardo Cockburn University of Minnesota

George M. Whitesides Harvard University

External Links

Wikipedia of Douglas N. Arnold Personal website of Douglas N. Arnold Google Scholar page

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