World's Best Scientists 2026 revealed!

Overview

Johnny Guzmán is affiliated with Brown University in the United States, focusing on research within the fields of Engineering and Mathematics. Their work primarily spans subfields such as Computational Mechanics, Numerical Analysis, Computational Theory and Mathematics, Mechanics of Materials, and Applied Mathematics.

The main topics covered in Guzmán's research include:

  • Advanced Numerical Methods in Computational Mathematics
  • Advanced Mathematical Modeling in Engineering
  • Numerical methods for differential equations
  • Differential Equations and Numerical Methods
  • Computational Fluid Dynamics and Aerodynamics
  • Advanced Numerical Analysis Techniques
  • Numerical methods in engineering

Guzmán has published multiple papers, including recent works such as:

  • "Exact smooth piecewise polynomial sequences on Alfeld splits," 2020, Mathematics of Computation
  • "Exact sequences on Powell-Sabin splits," 2020, CALCOLO
  • "Low-order divergence-free approximations for the Stokes problem on Worsey-Farin and Powell-Sabin splits," 2021, Computer Methods in Applied Mechanics and Engineering
  • "Fully discrete loosely coupled Robin-Robin scheme for incompressible fluid-structure interaction: stability and error analysis," 2022, Numerische Mathematik
  • "Stability and error analysis of a splitting method using Robin-Robin coupling applied to a fluid-structure interaction problem," 2021, Numerical Methods for Partial Differential Equations

The frequent publication venues for their work include:

  • arXiv (Cornell University)
  • IMA Journal of Numerical Analysis
  • Mathematics of Computation
  • SIAM Journal on Numerical Analysis
  • Journal of Numerical Mathematics

Among frequent coauthors who collaborate with Guzmán are:

  • Erik Burman
  • Michael Neilan
  • R. Durst
  • Sining Gong
  • Gabriel R. Barrenechea

Their scholarly contributions emphasize numerical and computational methods applied to engineering mathematics and fluid dynamics, with particular attention to stability, error analysis, and approximation on complex mesh splits and fluid-structure interaction problems.

Best Publications

  • A SUPERCONVERGENT LDG-HYBRIDIZABLE GALERKIN METHOD FOR SECOND-ORDER ELLIPTIC PROBLEMS

    Bernardo Cockburn;Bo Dong;Johnny Guzmán

  • A Hybridizable Discontinuous Galerkin Method for Steady-State Convection-Diffusion-Reaction Problems

    Bernardo Cockburn;Bo Dong;Johnny Guzmán;Marco Restelli

  • Superconvergent discontinuous Galerkin methods for second-order elliptic problems

    Bernardo Cockburn;Johnny Guzmán;Haiying Wang

  • Conforming and divergence-free Stokes elements on general triangular meshes

    Johnny Guzmán;Michael Neilan

  • A new elasticity element made for enforcing weak stress symmetry

    Bernardo Cockburn;Jayadeep Gopalakrishnan;Johnny Guzmán

  • Conforming and divergence-free Stokes elements in three dimensions

    Johnny Guzmán;Michael Neilan

  • Optimal Convergence of the Original DG Method for the Transport-Reaction Equation on Special Meshes

    Bernardo Cockburn;Bo Dong;Johnny Guzmán

  • A Second Elasticity Element Using the Matrix Bubble

    Jay Gopalakrishnan;Johnny Guzmán

  • An Analysis of the Embedded Discontinuous Galerkin Method for Second-Order Elliptic Problems

    Bernardo Cockburn;Johnny Guzmán;See-Chew Soon;Henry K. Stolarski

  • Symmetric Nonconforming Mixed Finite Elements for Linear Elasticity

    J. Gopalakrishnan;J. Guzmán

  • A Hybridizable and Superconvergent Discontinuous Galerkin Method for Biharmonic Problems

    Bernardo Cockburn;Bo Dong;Johnny Guzmán

  • The Scott-Vogelius finite elements revisited

    Johnny Guzman;L. Ridgway Scott

  • Inf-sup stability of geometrically unfitted Stokes finite elements

    Johnny Guzmán;Maxim A. Olshanskii

  • LOCAL ENERGY ESTIMATES FOR THE FINITE ELEMENT METHOD ON SHARPLY VARYING GRIDS

    Alan Demlow;Johnny Guzmán;Alfred H. Schatz

  • Inf-Sup Stable Finite Elements on Barycentric Refinements Producing Divergence--Free Approximations in Arbitrary Dimensions

    Johnny Guzmán;Michael Neilan

  • A Unified Analysis of Several Mixed Methods for Elasticity with Weak Stress Symmetry

    J. Guzmán

  • Hölder estimates for Green’s functions on convex polyhedral domains and their applications to finite element methods

    J. Guzmán;D. Leykekhman;J. Rossmann;A. H. Schatz

  • A Finite Element Method for High-Contrast Interface Problems with Error Estimates Independent of Contrast

    Johnny Guzmán;Manuel A. Sánchez;Marcus Sarkis

  • H(div) conforming and DG methods for incompressible Euler’s equations

    Johnny Guzmán;Chi-Wang Shu;Filánder A. Sequeira

  • Exact smooth piecewise polynomial sequences on Alfeld splits

    Guosheng Fu;Johnny Guzmán;Michael Neilan

Frequent Co-Authors

Erik Burman
Erik Burman University College London
Bernardo Cockburn
Bernardo Cockburn University of Minnesota
Maxim A. Olshanskii
Maxim A. Olshanskii University of Houston
Douglas N. Arnold
Douglas N. Arnold University of Minnesota
A. H. Schatz
A. H. Schatz Cornell University
Mark Ainsworth
Mark Ainsworth Brown University
Richard S. Falk
Richard S. Falk Rutgers, The State University of New Jersey
Chi-Wang Shu
Chi-Wang Shu Brown University
Santiago Badia
Santiago Badia Monash University
Béatrice Rivière
Béatrice Rivière Rice University

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 pursuing Mathematics in the USA, exploring related online degrees can open diverse career opportunities. Many opt for business-oriented programs, such as the easiest MBA specialization, which blends quantitative skills with management expertise. This path is ideal for those interested in leadership roles within finance, technology, or analytics sectors.

Additionally, the rise of online education platforms has made it possible to enroll in easy online MBA programs, offering flexible and accessible learning schedules. These programs are designed to accommodate working professionals and can significantly enhance one’s strategic and analytical thinking skills.

For those targeting higher business leadership, DBA online programs provide an advanced pathway to deepen expertise in business administration, useful for academic, consulting, or executive roles. These doctoral programs emphasize research and applied leadership, directly complementing a mathematical background.

Moreover, the integration of Mathematics with finance is increasingly popular, with affordable options available like the best online masters in finance. This degree equips students to excel in areas such as risk management, investment analysis, and financial modeling by leveraging strong mathematical foundations.

Best Scientists Citing Johnny Guzmán

Trending Scientists

Recently Published Articles