2026 Ragnar Winther: Mathematics Researcher – H-Index, Publications & Awards

Discipline name	D-Index	World Ranking	Current World Ranking	National Ranking	Current National Ranking	Publications	Citations
Mathematics	41	1878	1638	12	11	95	8998

Discipline name

D-Index

World Ranking

Current World Ranking

National Ranking

Current National Ranking

Publications

Citations

Mathematics

1878

1638

8998

Research.com Recognitions

2013 - Fellow of the American Mathematical Society

Overview

Ragnar Winther is affiliated with the University of Oslo in Norway and has contributed extensively to the fields of engineering and mathematics. Their research primarily focuses on computational mechanics, computational theory and mathematics, and geometry and topology.

The scientist's work spans several main topics, including:

Advanced Numerical Methods in Computational Mathematics
Advanced Numerical Analysis Techniques
Elasticity and Material Modeling
Algebraic Geometry and Number Theory
Nonlinear Waves and Solitons
Mathematical Analysis and Transform Methods
Matrix Theory and Algorithms

Winther's recent publications have appeared in a variety of venues, reflecting a broad engagement with computational and mathematical research areas. These venues include:

arXiv (Cornell University)
Foundations of Computational Mathematics
SIAM Journal on Numerical Analysis
Journal of Computational Mathematics
Mathematics of Computation

Selected recent papers authored or co-authored by Winther include:

The Bubble Transform and the de Rham Complex, 2022, published in Foundations of Computational Mathematics
A Uniform Preconditioner for a Newton Algorithm for Total Variation Minimization and Minimum-Surface Problems, 2023, published in SIAM Journal on Numerical Analysis
Well-Conditioned Frames for High Order Finite Element Methods, 2021, published in Journal of Computational Mathematics
Construction of polynomial preserving cochain extensions by blending, 2022, published on arXiv (Cornell University)
The Bubble Transform and the de Rham Complex, 2021, published on arXiv (Cornell University)

Frequent collaborators in Winther's research include:

Richard S. Falk
Xue-Cheng Tai
Weiying Zheng
Xiaodi Zhang
Kaibo Hu

Winther has been recognized by peers through election as a Fellow of the American Mathematical Society, an honor received in 2013. This accolade identifies contributions to the mathematical sciences 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
Mixed finite elements for elasticity

Douglas N. Arnold;Ragnar Winther

504
Citations
A preconditioned iterative method for saddlepoint problems

Torgeir Rusten;Ragnar Winther

401
Citations
Mixed finite element methods for linear elasticity with weakly imposed symmetry

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

366
Citations
Preconditioning discretizations of systems of partial differential equations

Kent-Andre Mardal;Ragnar Winther

340
Citations
Introduction to Partial Differential Equations: A Computational Approach

Aslak Tveito;Ragnar Winther

319
Citations
Preconditioning in H (div) and applications

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

289
Citations
A Robust Finite Element Method for Darcy--Stokes Flow

Kent Andre Mardal;Xue-Cheng Tai;Ragnar Winther

283
Citations
Finite elements for symmetric tensors in three dimensions

Douglas N. Arnold;Gerard Awanou;Ragnar Winther

209
Citations
Numerical methods for incompressible viscous flow

Hans Petter Langtangen;Hans Petter Langtangen;Kent-Andre Mardal;Kent-Andre Mardal;Ragnar Winther

177
Citations
The Korteweg–de Vries Equation, Posed in a Quarter-Plane

Jerry Bona;Ragnar Winther

172
Citations
A robust nonconforming H 2 -element

Trygve K. Nilssen;Xue-Cheng Tai;Ragnar Winther

169
Citations
NONCONFORMING MIXED ELEMENTS FOR ELASTICITY

Douglas N. Arnold;Ragnar Winther

166
Citations
Parameter-robust discretization and preconditioning of Biot's consolidation model

Jeonghun J. Lee;Kent-Andre Mardal;Ragnar Winther

154
Citations
Some Superlinear Convergence Results for the Conjugate Gradient Method

Ragnar Winther

140
Citations
Unified finite element discretizations of coupled Darcy–Stokes flow

Trygve Karper;Kent-Andre Mardal;Kent-Andre Mardal;Ragnar Winther

138
Citations
SMOOTHED PROJECTIONS IN FINITE ELEMENT EXTERIOR CALCULUS

Snorre H. Christiansen;Ragnar Winther

138
Citations
Robust convergence of multi point flux approximation on rough grids

Runhild A. Klausen;Ragnar Winther

136
Citations
Multigrid inH(div) andH(curl )

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

5
Citations

Frequent Co-Authors

Douglas N. Arnold University of Minnesota

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

Xue-Cheng Tai NORCE Research

Panayot S. Vassilevski Lawrence Livermore National Laboratory

Jerry L. Bona University of Illinois at Chicago

Joachim Schöberl TU Wien

Tom Lyche University of Oslo

External Links

Wikipedia of Ragnar Winther Personal website of Ragnar Winther

If you think any of the details on this page are incorrect, let us know.

Related Online Degrees & Career Pathways

For students pursuing Mathematics in the USA, exploring related online degrees can open diverse career pathways in business, finance, and data analysis. Many professionals complement their mathematical skills with advanced degrees that offer flexibility and affordability.

If you are looking for business-focused programs, options like the easiest mba programs provide a less competitive admission process, making it simpler to transition into management roles. Similarly, the easiest and fastest online mba degree programs offer accelerated formats for those eager to advance their careers quickly without compromising quality.

For those interested in higher-level leadership or academic roles, most affordable online dba programs provide doctorate-level credentials at a reasonable cost, ideal for mathematicians aiming to combine business acumen with their analytical expertise.

Additionally, the financial sector offers excellent opportunities for math graduates. Pursuing the cheapest online master's in finance allows you to gain specialized financial knowledge while managing expenses, strengthening your qualifications for roles in investment, risk management, and financial modeling.