World's Best Scientists 2026 revealed!

D-Index & Metrics

Mathematics

D-Index
46
Citations
7651
World Ranking
1374
National Ranking
611

Engineering and Technology

D-Index
46
Citations
7695
World Ranking
5188
National Ranking
1468

Overview

William Layton is a researcher affiliated with the University of Pittsburgh in the United States. Their work primarily falls within the field of Engineering, with a particular focus on Computational Mechanics, Numerical Analysis, and Atmospheric Science. Other subfields include Computational Theory and Mathematics as well as Environmental Engineering.

The main research topics covered by Layton involve advanced numerical methods in computational mathematics, computational fluid dynamics and aerodynamics, as well as fluid dynamics and turbulent flows. Additional interests include numerical methods for differential equations, meteorological phenomena and simulations, matrix theory and algorithms, and studies related to wind and air flow.

Layton has contributed to several recent publications, including:

  • "Adaptive partitioned methods for the time-accurate approximation of the evolutionary Stokes-Darcy system," 2020, published in Computer Methods in Applied Mechanics and Engineering
  • "A Variable Stepsize, Variable Order Family of Low Complexity," 2021, published in SIAM Journal on Scientific Computing
  • "On the Foundations of Eddy Viscosity Models of Turbulence," 2020, published in Fluids
  • "A general linear method approach to the design and optimization of efficient, accurate, and easily implemented time-stepping methods in CFD," 2022, published in Journal of Computational Physics
  • "Time step adaptivity in the method of Dahlquist, Liniger and Nevanlinna," 2023, published in Advances in Computational Science and Engineering

Their coauthors include Aytekin Çıbık, Cătălin Trenchea, Rui Fang, Michael McLaughlin, and Michael Schneier, with multiple collaborations reflecting ongoing research partnerships.

Layton has published in prominent venues such as arXiv (Cornell University), Numerical Methods for Partial Differential Equations, Computer Methods in Applied Mechanics and Engineering, Applied Mathematics Letters, and SSRN Electronic Journal.

In addition to journal articles, Layton is an author of a book titled Numerical Linear Algebra, published in 2020 by World Scientific, which has gained citation recognition.

Best Publications

  • Coupling Fluid Flow with Porous Media Flow

    William J. Layton;Friedhelm Schieweck;Ivan Yotov

  • Mathematics of large eddy simulation of turbulent flows

    Luigi Carlo Berselli;T Iliescu;W. J. Layton

  • Introduction to the Numerical Analysis of Incompressible Viscous Flows

    William Layton

  • A Two-Level Method with Backtracking for the Navier--Stokes Equations

    W. Layton;L. Tobiska

  • A two-level discretization method for the Navier-Stokes equations

    W. Layton

  • A connection between subgrid scale eddy viscosity and mixed methods

    W. Layton

  • APPROXIMATION OF THE LARGER EDDIES IN FLUID MOTIONS II: A MODEL FOR SPACE-FILTERED FLOW

    Giovanni P. Galdi;William J. Layton

  • An analysis of the finite element method for natural convection problems

    J. Boland;W. Layton

  • A two-level variational multiscale method for convection-dominated convection-diffusion equations

    Volker John;Songul Kaya;William Layton

  • On the accuracy of the rotation form in simulations of the Navier-Stokes equations

    William Layton;Carolina C. Manica;Monika Neda;Maxim Olshanskii

  • Approximate Deconvolution Models of Turbulence: Analysis, Phenomenology and Numerical Analysis

    William J. Layton;Leo G. Rebholz

  • Analysis of Long Time Stability and Errors of Two Partitioned Methods for Uncoupling Evolutionary Groundwater--Surface Water Flows

    William J. Layton;Hoang Tran;Catalin Trenchea

  • A decoupling method with different subdomain time steps for the nonstationary stokes–darcy model

    Li Shan;Haibiao Zheng;William J. Layton

  • On a well-posed turbulence model

    William J. Layton;Roger Lewandowski

  • Error analysis for finite element methods for steady natural convection problems

    J. Boland;W. Layton

  • Two-level Picard and modified Picard methods for the Navier-Stokes equations

    W. Layton;W. Lenferink

  • Numerical analysis and computational testing of a high accuracy Leray‐deconvolution model of turbulence

    William Layton;Carolina C. Manica;Monika Neda;Leo G. Rebholz

  • A defect-correction method for the incompressible Navier-Stokes equations

    W. Layton;H. K. Lee;J. Peterson

  • A Two-Level Method for the Discretization of Nonlinear Boundary Value Problems

    O. Axelsson;W. Layton

  • A multilevel mesh independence principle for the Navier-Stokes equations

    W. Layton;H. W. J. Lenferink

Frequent Co-Authors

Volker John
Volker John Freie Universität Berlin
Traian Iliescu
Traian Iliescu Virginia Tech
Mihai Anitescu
Mihai Anitescu Argonne National Laboratory
Béatrice Rivière
Béatrice Rivière Rice University
Giovanni P. Galdi
Giovanni P. Galdi University of Pittsburgh
Lutz Tobiska
Lutz Tobiska Otto-von-Guericke University Magdeburg
Ivan Yotov
Ivan Yotov University of Pittsburgh
Qiang Du
Qiang Du Columbia University
Maxim A. Olshanskii
Maxim A. Olshanskii University of Houston
Caterina Rosano
Caterina Rosano University of Pittsburgh

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

Report an issue

We appreciate your kind effort to assist us to improve this page, it would be helpful providing us with as much detail as possible in the text box below:

Related Online Degrees & Career Pathways

For students studying Mathematics in the USA, exploring related online degrees can expand career opportunities in fields like finance, business, and marketing. Pursuing a cheap masters in finance is a practical option that complements strong quantitative skills and opens doors to roles in investment analysis, financial planning, and risk management.

If you’re looking for flexible but fast-paced graduate programs, consider the shortest online mba programs, which allow professionals to quickly gain essential business leadership abilities without putting their careers on hold.

Marketing is another strong pathway for math graduates, especially those interested in data-driven decision-making. Earning an online marketing degree can provide valuable skills in analytics, customer insight, and strategy, often coupled with attractive earning potential.

For those who prefer an accelerated business focus, the cheapest 1 year online mba programs offer a cost-effective and time-efficient pathway to boost leadership credentials and apply mathematical expertise to strategic decision-making roles.

Best Scientists Citing William Layton

Trending Scientists

Recently Published Articles