2026 Richard S. Falk: Mathematics Researcher – H-Index, Publications & Awards

Discipline name	D-Index	World Ranking	Current World Ranking	National Ranking	Current National Ranking	Publications	Citations
Mathematics	40	2002	1757	845	694	87	9667

Research.com Recognitions

2019 - Fellow of the American Mathematical Society For contributions to numerical analysis and for service to the mathematical community.
2012 - SIAM Fellow For contributions to the understanding of the stability and convergence properties of the finite element method, and for service to the numerical analysis community.

Overview

Richard S. Falk is affiliated with Rutgers, The State University of New Jersey in the United States. Their research contributions primarily focus on mathematics, with an emphasis on computational mechanics, geometry and topology, computational theory and mathematics, mathematical physics, and numerical analysis.

The scientist's research addresses a range of topics within mathematics. Notable areas include:

Advanced Numerical Analysis Techniques
Algebraic Geometry and Number Theory
Mathematical Dynamics and Fractals
Nonlinear Waves and Solitons
Mathematical Analysis and Transform Methods
Polynomial and algebraic computation
Iterative Methods for Nonlinear Equations

Richard S. Falk has contributed several papers published in various venues. Recent publications include:

The Bubble Transform and the de Rham Complex, 2022, Foundations of Computational Mathematics
Hidden positivity and a new approach to numerical computation of Hausdorff dimension: higher order methods, 2021, Journal of Fractal Geometry Mathematics of Fractals and Related Topics
Construction of polynomial preserving cochain extensions by blending, 2022, arXiv (Cornell University)
The Bubble Transform and the de Rham Complex, 2021, arXiv (Cornell University)
Hidden Positivity and a New Approach to Numerical Computation of Hausdorff Dimension: Higher Order Methods, 2020, arXiv (Cornell University)

Their work has appeared frequently in the following publication venues:

arXiv (Cornell University)
Foundations of Computational Mathematics
Journal of Fractal Geometry Mathematics of Fractals and Related Topics
Mathematics of Computation

Collaboration is evident in their frequent co-authors, which include:

Ragnar Winther
Roger D. Nussbaum

Recognition of their work includes being named a Fellow of the American Mathematical Society in 2019 for contributions to numerical analysis and for service to the mathematical community.

Additionally, Richard S. Falk was recognized as a SIAM Fellow in 2012 for work related to the stability and convergence properties of the finite element method, along with their service to the numerical analysis community.

Best Publications

Finite element exterior calculus, homological techniques, and applications

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

1214
Citations
Finite element exterior calculus: From hodge theory to numerical stability

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

870
Citations
Multigrid in H(div) and H(curl)

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

540
Citations
Error estimates for the approximation of a class of variational inequalities

Richard S. Falk

467
Citations
A uniformly accurate finite element method for the Reissner-Mindlin plate

D. N. Arnold;R. S. Falk

390
Citations
Approximation of a class of optimal control problems with order of convergence estimates

Richard S. Falk

378
Citations
Mixed finite element methods for linear elasticity with weakly imposed symmetry

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

366
Citations
Error estimates for mixed methods

R. S. Falk;J. E. Osborn

350
Citations
Approximation by quadrilateral finite elements

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

344
Citations
Basic principles of mixed Virtual Element Methods

F. Brezzi;Richard S. Falk;L. Donatella Marini

323
Citations
Quadrilateral H (div) Finite Elements

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

310
Citations
Preconditioning in H (div) and applications

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

289
Citations
Mixed Finite Elements, Compatibility Conditions, and Applications

Daniele Boffi;Franco Brezzi;Leszek F. Demkowicz;Ricardo G. Durán

252
Citations
Stability of higher-order Hood-Taylor methods

Franco Brezzi;Richard S. Falk

247
Citations
Nonconforming finite element methods for the equations of linear elasticity

Richard S. Falk

240
Citations
Stokes Complexes and the Construction of Stable Finite Elements with Pointwise Mass Conservation

Richard S. Falk;Michael Neilan

189
Citations
Asymptotic analysis of the boundary layer for the Reissner-Mindlin plate model

Douglas N. Arnold;Richard S. Falk

172
Citations
The boundary layer for the reissner-mindlin plate model

Douglas N. Arnold;Richard S. Falk

142
Citations
Explicit Finite Element Methods for Symmetric Hyperbolic Equations

Richard S. Falk;Gerard R. Richter

142
Citations
A new mixed formulation for elasticity

Douglas N. Arnold;Richard S. Falk

139
Citations
Approximation by quadrilateral finite elements

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

3
Citations

Frequent Co-Authors

Douglas N. Arnold University of Minnesota

Ragnar Winther University of Oslo

Roger D. Nussbaum Rutgers, The State University of New Jersey

Richard E. Ewing Texas A&M University

Franco Brezzi National Research Council (CNR)

Daniele Boffi King Abdullah University of Science and Technology

Bernard D. Coleman Rutgers, The State University of New Jersey

Peter Monk University of Delaware

Michael Holst University of California, San Diego

Harald Niederreiter Austrian Academy of Sciences

External Links

Personal website of Richard S. Falk Google Scholar page

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