My main research interest lies in the area of numerical approximations to partial differential equations (PDEs). I work in devising new numerical methods for various PDEs and analyzing new or existing numerical methods. Recently my focus has been on finite element exterior calculus (FEEC).
| Guzmán, Johnny, Lischke, Anna, Neilan, Michael. "Exact sequences on Worsey–Farin splits." Mathematics of Computation, 2022. |
| Salazar Coariti, Adriana C., Fabien, Maurice S., Guzman, Johnny, McGuire, Jeffrey A., De Vita, Raffaella, Toussaint, Kimani C. "Fluid mechanics approach to analyzing collagen fiber organization." Journal of Biomedical Optics, vol. 27, no. 01, 2022. |
| Burman, Erik, Durst, Rebecca, Fernández, Miguel A., Guzmán, Johnny. "Fully discrete loosely coupled Robin-Robin scheme for incompressible fluid–structure interaction: stability and error analysis." Numerische Mathematik, 2022. |
| Burman, Erik, Guzmán, Johnny. "Implicit-explicit multistep formulations for finite element discretisations using continuous interior penalty." ESAIM: Mathematical Modelling and Numerical Analysis, vol. 56, no. 1, 2022, pp. 349-383. |
| Fabien, Maurice, Guzmán, Johnny, Neilan, Michael, Zytoon, Ahmed. "Low-order divergence-free approximations for the Stokes problem on Worsey–Farin and Powell–Sabin splits." Computer Methods in Applied Mechanics and Engineering, vol. 390, 2022, pp. 114444. |
| Ahmed, Naveed, Barrenechea, Gabriel R., Burman, Erik, Guzmán, Johnny, Linke, Alexander, Merdon, Christian. "A Pressure-Robust Discretization of Oseen's Equation Using Stabilization in the Vorticity Equation." SIAM Journal on Numerical Analysis, vol. 59, no. 5, 2021, pp. 2746-2774. |
| Guzmán, Johnny, Salgado, Abner J. "Estimation of the continuity constants for Bogovskiĭ and regularized Poincaré integral operators." Journal of Mathematical Analysis and Applications, vol. 502, no. 1, 2021, pp. 125246. |
| Arnold, Douglas, Guzmán, Johnny. "Local L2-bounded commuting projections in FEEC." ESAIM: Mathematical Modelling and Numerical Analysis, vol. 55, no. 5, 2021, pp. 2169-2184. |
| Burman, Erik, Durst, Rebecca, Guzmán, Johnny. "Stability and error analysis of a splitting method using Robin – Robin coupling applied to a fluid–structure interaction problem." Numerical Methods for Partial Differential Equations, 2021. |
| Fu, Guosheng, Guzmán, Johnny, Neilan, Michael. "Exact smooth piecewise polynomial sequences on Alfeld splits." Mathematics of Computation, vol. 89, no. 323, 2020, pp. 1059-1091. |
| Barrenechea, Gabriel, Burman, Erik, Guzmán, Johnny. "Well-posedness and H(div)-conforming finite element approximation of a linearised model for inviscid incompressible flow." Mathematical Models and Methods in Applied Sciences, vol. 30, no. 05, 2020, pp. 847-865. |
| Guzmán, Johnny, Neilan, Michael. "Inf-Sup Stable Finite Elements on Barycentric Refinements Producing Divergence--Free Approximations in Arbitrary Dimensions." SIAM Journal on Numerical Analysis, vol. 56, no. 5, 2018, pp. 2826-2844. |
| Guzmán, Johnny, Scott, L. Ridgway. "The Scott-Vogelius finite elements revisited." Mathematics of Computation, vol. 88, no. 316, 2018, pp. 515-529. |
| Guzmán, Johnny, Sánchez, Manuel A., Sarkis, Marcus. "A Finite Element Method for High-Contrast Interface Problems with Error Estimates Independent of Contrast." Journal of Scientific Computing, vol. 73, no. 1, 2017, pp. 330-365. |
| Guzman, Johnny, Madureira, Alexandre, Sarkis, Marcus, Walker, Shawn. "Analysis of the Finite Element Method for the Laplace–Beltrami Equation on Surfaces with Regions of High Curvature Using Graded Meshes." Journal of Scientific Computing, vol. 77, no. 3, 2017, pp. 1736-1761. |
| Guzmán, Johnny, Olshanskii, Maxim. "Inf-sup stability of geometrically unfitted Stokes finite elements." Mathematics of Computation, vol. 87, no. 313, 2017, pp. 2091-2112. |
| Burman, Erik, Guzmán, Johnny, Sánchez, Manuel A, Sarkis, Marcus. "Robust flux error estimation of an unfitted Nitsche method for high-contrast interface problems." IMA Journal of Numerical Analysis, vol. 38, no. 2, 2017, pp. 646-668. |
| Gottlieb, Sigal, Guzmán, Johnny, Li, Fengyan, Ryan, Jennifer K. "Special Issue in Honor of Professor Chi-Wang Shu." Journal of Scientific Computing, vol. 73, no. 2-3, 2017, pp. 459-460. |
| Guzmán, Johnny, Shu, Chi-Wang, Sequeira, Filánder A. "H(div) conforming and DG methods for incompressible Euler’s equations." IMA Journal of Numerical Analysis, 2016, pp. drw054. |
| Guzmán, Johnny, Sánchez, Manuel A., Sarkis, Marcus. "Higher-order finite element methods for elliptic problems with interfaces." ESAIM: Mathematical Modelling and Numerical Analysis, vol. 50, no. 5, 2016, pp. 1561-1583. |
| Guzmán, Johnny, Klivans, Caroline. "Chip-firing and energy minimization on M-matrices." Journal of Combinatorial Theory, Series A, vol. 132, 2015, pp. 14-31. |
| Guzmán, Johnny, Sánchez, Manuel A. "Max-Norm Stability of Low Order Taylor–Hood Elements in Three Dimensions." J Sci Comput, vol. 65, no. 2, 2015, pp. 598-621. |
| Guzmán, Johnny, Sánchez, Manuel A., Sarkis, Marcus. "On the accuracy of finite element approximations to a class of interface problems." Mathematics of Computation, vol. 85, no. 301, 2015, pp. 2071-2098. |
| Gudi, Thirupathi, Guzmán, Johnny. "Convergence analysis of the lowest order weakly penalized adaptive discontinuous Galerkin methods." ESAIM: M2AN, vol. 48, no. 3, 2014, pp. 753-764. |
| Zhang, Yifan, Wang, Wei, Guzmán, Johnny, Shu, Chi-Wang. "Multi-scale Discontinuous Galerkin Method for Solving Elliptic Problems with Curvilinear Unidirectional Rough Coefficients." J Sci Comput, vol. 61, no. 1, 2014, pp. 42-60. |
| Arnold, Douglas N., Falk, Richard S., Guzmán, Johnny, Tsogtgerel, Gantumur. "On the consistency of the combinatorial codifferential." Trans. Amer. Math. Soc., vol. 366, no. 10, 2014, pp. 5487-5502. |
| Guzman, J., Neilan, M. "Conforming and divergence-free Stokes elements in three dimensions." IMA Journal of Numerical Analysis, vol. 34, no. 4, 2013, pp. 1489-1508. |
| Guzmán, Johnny, Neilan, Michael. "Conforming and divergence-free Stokes elements on general triangular meshes." Mathematics of Computation, vol. 83, no. 285, 2013, pp. 15-36. |
| Badia, S., Codina, R., Gudi, T., Guzman, J. "Error analysis of discontinuous Galerkin methods for the Stokes problem under minimal regularity." IMA Journal of Numerical Analysis, vol. 34, no. 2, 2013, pp. 800-819. |
| Guzmán, Johnny, Neilan, Michael. "Symmetric and conforming mixed finite elements for plane elasticity using rational bubble functions." Numer. Math., vol. 126, no. 1, 2013, pp. 153-171. |
| Johnny, G., Michael, N. "A family of nonconforming elements for the Brinkman problem." IMA Journal of Numerical Analysis, vol. 32, no. 4, 2012, pp. 1484-1508. |
| Guzmán, Johnny, Salgado, Abner J., Sayas, Francisco-Javier. "A Note on the Ladyženskaja-Babuška-Brezzi Condition." J Sci Comput, vol. 56, no. 2, 2012, pp. 219-229. |
| Cockburn, Bernardo, Guzmán, Johnny, Sayas, Francisco-Javier. "Coupling of Raviart--Thomas and Hybridizable Discontinuous Galerkin Methods with BEM." SIAM Journal on Numerical Analysis, vol. 50, no. 5, 2012, pp. 2778-2801. |
| Guzmán, J., Leykekhman, D. "Pointwise error estimates of finite element approximations to the Stokes problem on convex polyhedra." Mathematics of Computation, vol. 81, no. 280, 2012, pp. 1879-1902. |
| Guzmán, Johnny, Leykekhman, Dmitriy, Neilan, Michael. "A family of non-conforming elements and the analysis of Nitsche’s method for a singularly perturbed fourth order problem." Calcolo, vol. 49, no. 2, 2011, pp. 95-125. |
| Behrens, Edwin M., Guzmán, Johnny. "A Mixed Method for the Biharmonic Problem Based On a System of First-Order Equations." SIAM Journal on Numerical Analysis, vol. 49, no. 2, 2011, pp. 789-817. |
| Gopalakrishnan, J., Guzman, J. "A second elasticity element using the matrix bubble." IMA Journal of Numerical Analysis, vol. 32, no. 1, 2011, pp. 352-372. |
| Gopalakrishnan, J., Guzmán, J. "Symmetric Nonconforming Mixed Finite Elements for Linear Elasticity." SIAM Journal on Numerical Analysis, vol. 49, no. 4, 2011, pp. 1504-1520. |
| Cockburn, Bernardo, Gopalakrishnan, Jayadeep, Guzmán, Johnny. "A new elasticity element made for enforcing weak stress symmetry." Mathematics of Computation, vol. 79, no. 271, 2010, pp. 1331-1349. |
| Behrens, Edwin M., Guzmán, J. "A New Family of Mixed Methods for the Reissner-Mindlin Plate Model Based on a System of First-Order Equations." J Sci Comput, vol. 49, no. 2, 2010, pp. 137-166. |
| Guzmán, J. "A Unified Analysis of Several Mixed Methods for Elasticity with Weak Stress Symmetry." J Sci Comput, vol. 44, no. 2, 2010, pp. 156-169. |
| Demlow, Alan, Guzmán, Johnny, Schatz, Alfred H. "Local energy estimates for the finite element method on sharply varying grids." Mathematics of Computation, vol. 80, no. 273, 2010, pp. 1-9. |
| Cockburn, Bernardo, Dong, Bo, Guzmán, Johnny, Qian, Jianliang. "Optimal Convergence of the Original DG Method on Special Meshes for Variable Transport Velocity." SIAM Journal on Numerical Analysis, vol. 48, no. 1, 2010, pp. 133-146. |
| Cockburn, Bernardo, Dong, Bo, Guzmán, Johnny. "A Hybridizable and Superconvergent Discontinuous Galerkin Method for Biharmonic Problems." J Sci Comput, vol. 40, no. 1-3, 2009, pp. 141-187. |
| Cockburn, Bernardo, Dong, Bo, Guzmán, Johnny, Restelli, Marco, Sacco, Riccardo. "A Hybridizable Discontinuous Galerkin Method for Steady-State Convection-Diffusion-Reaction Problems." SIAM J. Sci. Comput., vol. 31, no. 5, 2009, pp. 3827-3846. |
| Cockburn, Bernardo, Guzmán, Johnny, Soon, See-Chew, Stolarski, Henry K. "An Analysis of the Embedded Discontinuous Galerkin Method for Second-Order Elliptic Problems." SIAM Journal on Numerical Analysis, vol. 47, no. 4, 2009, pp. 2686-2707. |
| Guzmán, J., Leykekhman, D., Rossmann, J., Schatz, A. H. "Hölder estimates for Green’s functions on convex polyhedral domains and their applications to finite element methods." Numer. Math., vol. 112, no. 2, 2009, pp. 221-243. |
| Cockburn, Bernardo, Guzmán, Johnny, Wang, Haiying. "Superconvergent discontinuous Galerkin methods for second-order elliptic problems." Mathematics of Computation, vol. 78, no. 265, 2009, pp. 1-1. |
| Cockburn, Bernardo, Dong, Bo, Guzmán, Johnny. "A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems." Mathematics of Computation, vol. 77, no. 264, 2008, pp. 1887-1916. |
| Cockburn, Bernardo, Guzmán, Johnny. "Error Estimates for the Runge–Kutta Discontinuous Galerkin Method for the Transport Equation with Discontinuous Initial Data." SIAM Journal on Numerical Analysis, vol. 46, no. 3, 2008, pp. 1364-1398. |
| Guzmán, J. "Local and pointwise error estimates of the local discontinuous Galerkin method applied to the Stokes problem." Mathematics of Computation, vol. 77, no. 263, 2008, pp. 1293-1322. |
| Cockburn, Bernardo, Dong, Bo, Guzmán, Johnny. "Optimal Convergence of the Original DG Method for the Transport-Reaction Equation on Special Meshes." SIAM Journal on Numerical Analysis, vol. 46, no. 3, 2008, pp. 1250-1265. |
| Guzmán, Johnny, Rivière, Béatrice. "Sub-optimal Convergence of Non-symmetric Discontinuous Galerkin Methods for Odd Polynomial Approximations." J Sci Comput, vol. 40, no. 1-3, 2008, pp. 273-280. |
| Burman, E., Guzman, J., Leykekhman, D. "Weighted error estimates of the continuous interior penalty method for singularly perturbed problems." IMA Journal of Numerical Analysis, vol. 29, no. 2, 2008, pp. 284-314. |
| Guzmán, J. "Local analysis of discontinuous Galerkin methods applied to singularly perturbed problems." Journal of Numerical Mathematics, vol. 14, no. 1, 2006. |
| Guzmán, Johnny. "Pointwise error estimates for discontinuous Galerkin methods with lifting operators for elliptic problems." Mathematics of Computation, vol. 75, no. 255, 2006, pp. 1067-1086. |
| Guzmán, J. "Quadrature and Schatz’s Pointwise Estimates for Finite Element Methods." BIT Numerical Mathematics, vol. 45, no. 4, 2005, pp. 695-707. |
Completed Grants
Current Grants
Recent Presentations
| Year | Degree | Institution |
|---|---|---|
| 2005 | PhD | Cornell University |
| 1999 | BS | California State University |
| Name | Title |
|---|---|
| Ainsworth, Mark | Francis Wayland Professor of Applied Mathematics |
| Klivans, Caroline | Professor of Applied Mathematics |
| Shu, Chi-Wang | Stowell University Professor of Applied Mathematics |
| Toussaint, Kimani | Thomas J. Watson, Sr. Professor of Science |
Membership
Society for Industrial and Applied Mathematics (SIAM)
Society for the Advancement of Chicanos and Native-Americans in Science (SACNAS)
American Mathematical Society (AMS)
Editorial Boards:
1) Journal of Numerical Mathematics
2) Journal of Scientific Computing (2014-2020)
3) Mathematical Models and Methods in Applied Sciences (M3AS)
4) Calcolo (2020-2026)
5) La Matematica (2021-2026)
| APMA 1170 - Introduction to Computational Linear Algebra |
| APMA 1180 - Introduction to Numerical Solution of Differential Equations |
| APMA 1720 - Monte Carlo Simulation with Applications to Finance |
| APMA 2550 - Numerical Solution of Partial Differential Equations I |
| APMA 2570A - Numerical Solution of Partial Differential Equations III |
| APMA 2570B - Numerical Solution of Partial Differential Equations III |
| APMA 2580A - Computational Fluid Dynamics |
| APMA 2811X - Finite Element Exterior Calculus |
| APMA 2811X - Finitite Element Exterior Calculus |
