Jehanzeb H. Chaudhry
Associate Professor of Mathematics and Statistics

Research Group

Graduate Students (Past and Current):

  • Michael Brown. Research Interest: Lattice Boltzmann Methods
  • Md Al Amin Molla. Research Interest: Differential Algebraic Equations
  • Trevor Giannini. Research Interest: Shallow Water Equations
  • Raghav Agrawal. Research Interest: Fluid Structure Interaction
  • Shandy Simpson. Research Interest: Moving Least Squares Methods
  • Mimi. Research Interests: Optimal Transport and Uncertainty Quantification
  • Z. Stevens. PhD Thesis: Robust Un-certainty Quantification with Analysis of Error in Standard and Non-standard Quantities of Interest
  • Danial Alcala. Masters Thesis: Derivation of Adjoint Based Error Estimates for Nonlinear Ordinary Differential Equations with Application to Multistage SIR Models with Demographics
  • Jonathan Gutierrez. Masters Thesis: Using Physics-Informed Neural Networks for Multigrid in Time Coarse Grid Equations
  • Ari Rappaport. Masters Thesis: A Posteriori error analysis for Magnetohydrodynamics.
  • Nicholas Abel. Masters Thesis: Multi-level Asymptotic Parallel-in-Time Techniques For Highly Oscillatory Hyperbolic PDEs..

Undergraduate Students (Past):

  • Christopher Leap. Deep learning for predicting Conjugate Gradient iterations for Uncertainty Quantification. Jupyter Notebook on Github
  • Ari Rappaport. Exploration of Black Box Multigrid for Linear Systems Modeling Resistive MHD, Honors Thesis, (2018)

Research Areas

Uncertainty Quantification and Error Estimation

  • Jehanzeb H. Chaudhry, Owen Lewis, Md Al Amin Molla. Adjoint-based a Posteriori Error Analysis for Semi-explicit Index-1 and Hessenberg Index-2 Differential-Algebraic Equations. BIT Numerical Mathematics (2026) [Preprint]

  • Nishant Panda, Jehanzeb H. Chaudhry, Natalie Klein, James Carzon, Troy Butler. Local Stochastic Sensitivity Analysis for Dynamical Systems. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR (2025) [Text]

  • Jehanzeb H. Chaudhry, Donald Estep, Simon J. Tavener. A Posteriori Error Analysis for a Space-Time Parallel Discretization of Parabolic Partial Differential Equations. Numerical Methods for Partial Differential Equations (2024) [Text, Preprint]

  • Jehanzeb H. Chaudhry, Donald Estep, Trevor Giannini, Zachary Stevens, Simon J. Tavener. Error Estimation for the Time to a Threshold Value in Evolutionary Partial Differential Equations. BIT Numerical Mathematics (2023) [Text, Preprint]

  • Jehanzeb H. Chaudhry, Zachary Stevens. Adjoint-based Adaptive Multi-Level Monte Carlo for Differential Equations. [Preprint]

  • Jehanzeb H. Chaudhry, Ari E. Rappaport, John N. Shadid. An a Posteriori Error Analysis for the Equations of Stationary Incompressible Magnetohydrodynamics. SIAM Journal on Scientific Computing (2021) [Text, Preprint]

  • Jehanzeb H. Chaudhry, Donald Estep, Simon J. Tavener. A Posteriori Error Analysis for Schwarz Overlapping Domain Decomposition Methods. BIT Numerical Mathematics (2021) [Text, Preprint]

  • Vicente Ramm, Jehanzeb H. Chaudhry, Christopher D. Cooper. Efficient Mesh Refinement for the Poisson–Boltzmann Equation with Boundary Elements. Journal of Computational Chemistry (2021) [Text, Preprint]

  • Jehanzeb H. Chaudhry, Donald Estep, Zachary Stevens, Simon J. Tavener. Error Estimation and Uncertainty Quantification for First Time to a Threshold Value. BIT Numerical Mathematics (2021) [Text, Preprint]

  • Jehanzeb H. Chaudhry, J. B. Collins. A Posteriori Error Estimation for the Spectral Deferred Correction Method. Journal of Computational and Applied Mathematics (2021) [Text, Preprint]

  • Jehanzeb H. Chaudhry, John N. Shadid, Timothy Wildey. A Posteriori Analysis of an IMEX Entropy-Viscosity Formulation for Hyperbolic Conservation Laws with Dissipation. Applied Numerical Mathematics (2019) [Text]

  • Jehanzeb H. Chaudhry. A Posteriori Analysis and Efficient Refinement Strategies for the Poisson–Boltzmann Equation. SIAM Journal on Scientific Computing (2018) [Text]

  • Jehanzeb H. Chaudhry, Nathanial Burch, Donald Estep. Efficient Distribution Estimation and Uncertainty Quantification for Elliptic Problems on Domains with Stochastic Boundaries. SIAM/ASA Journal on Uncertainty Quantification (2018) [Text]

  • Jehanzeb H. Chaudhry, J. B. Collins, John N. Shadid. A Posteriori Error Estimation for Multi-Stage Runge–Kutta IMEX Schemes. Applied Numerical Mathematics (2017) [Text]

  • Jehanzeb H. Chaudhry, Donald Estep, Max Gunzburger. Exploration of Efficient Reduced-Order Modeling and a Posteriori Error Estimation. International Journal for Numerical Methods in Engineering (2017) [Text]

  • Jehanzeb H. Chaudhry, Donald Estep, Simon J. Tavener, Varis Carey, J. Sandelin. A Posteriori Error Analysis of Two-Stage Computation Methods with Application to Efficient Discretization and the Parareal Algorithm. SIAM Journal on Numerical Analysis (2016) [Text]

  • Jehanzeb H. Chaudhry, Donald Estep, Victor Ginting, John N. Shadid, Simon J. Tavener. A Posteriori Error Analysis of IMEX Multi-Step Time Integration Methods for Advection-Diffusion-Reaction Equations. Computer Methods in Applied Mechanics and Engineering (2015) [Text]

  • Jehanzeb H. Chaudhry, Donald Estep, Victor Ginting, Simon J. Tavener. A Posteriori Analysis for Iterative Solvers for Nonautonomous Evolution Problems. SIAM/ASA Journal on Uncertainty Quantification (2015) [Text]

  • August Johansson, Jehanzeb H. Chaudhry, Varis Carey, Donald Estep, Victor Ginting, Mats G. Larson, Simon J. Tavener. Adaptive Finite Element Solution of Multiscale PDE–ODE Systems. Computer Methods in Applied Mechanics and Engineering (2015) [Text]

  • Jehanzeb H. Chaudhry, Donald Estep, Victor Ginting, Simon J. Tavener. A Posteriori Analysis of an Iterative Multi-Discretization Method for Reaction-Diffusion Systems. Computer Methods in Applied Mechanics and Engineering (2013) [Text]

Continuum Methods for Biomolecular Simulation

  • Martín A. Achondo, Jehanzeb H. Chaudhry, Christopher D. Cooper. An Investigation of Physics Informed Neural Networks to Solve the Poisson–Boltzmann Equation in Molecular Electrostatics. Journal of Chemical Theory and Computation (2025) [Text, Preprint]

  • Vicente Ramm, Jehanzeb H. Chaudhry, Christopher D. Cooper. Efficient Mesh Refinement for the Poisson–Boltzmann Equation with Boundary Elements. Journal of Computational Chemistry (2021) [Text, Preprint]

  • Divya Bohra, Jehanzeb H. Chaudhry, Thomas Burdyny, Evgeny A. Pidko, Wilson A. Smith. Modeling the Electrical Double Layer to Understand the Reaction Environment in a CO2 Electrocatalytic System. Energy & Environmental Science (2019) [Text]

  • Jehanzeb H. Chaudhry. A Posteriori Analysis and Efficient Refinement Strategies for the Poisson–Boltzmann Equation. SIAM Journal on Scientific Computing (2018) [Text]

  • Jehanzeb H. Chaudhry, Jeffrey Comer, Aleksei Aksimentiev, Luke N. Olson. A Stabilized Finite Element Method for Modified Poisson–Nernst–Planck Equations to Determine Ion Flow Through a Nanopore. Communications in Computational Physics (2014) [Text]

  • Jehanzeb H. Chaudhry, Stephen D. Bond, Luke N. Olson. A Weighted Adaptive Least-Squares Finite Element Method for the Poisson–Boltzmann Equation. Applied Mathematics and Computation (2012) [Text]

  • Jehanzeb H. Chaudhry, Stephen D. Bond, Luke N. Olson. Finite Element Approximation to a Finite-Size Modified Poisson–Boltzmann Equation. Journal of Scientific Computing (2011) [Text]

  • Stephen D. Bond, Jehanzeb H. Chaudhry, Eric C. Cyr, Luke N. Olson. A First-Order System Least-Squares Finite Element Method for the Poisson–Boltzmann Equation. Journal of Computational Chemistry (2010) [Text]

Reduced Order Modeling

  • Peter Sentz, Jehanzeb H. Chaudhry, Luke N. Olson. On Computing Coercivity Constants in Linear Variational Problems Through Eigenvalue Analysis. IMA Journal of Numerical Analysis (2025) [Text, Preprint]

  • Jehanzeb H. Chaudhry, Luke N. Olson, Peter Sentz. A Least-Squares Finite Element Reduced Basis Method. SIAM Journal on Scientific Computing (2021) [Text, Preprint]

  • Jehanzeb H. Chaudhry, Donald Estep, Max Gunzburger. Exploration of Efficient Reduced-Order Modeling and a Posteriori Error Estimation. International Journal for Numerical Methods in Engineering (2017) [Text]

Finite Element Method for PDEs

  • August Johansson, Jehanzeb H. Chaudhry, Varis Carey, Donald Estep, Victor Ginting, Mats G. Larson, Simon J. Tavener. Adaptive Finite Element Solution of Multiscale PDE–ODE Systems. Computer Methods in Applied Mechanics and Engineering (2015) [Text]

  • Anil N. Hirani, Kalyana B. Nakshatrala, Jehanzeb H. Chaudhry. Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus. International Journal for Computational Methods in Engineering Science and Mechanics (2015) [Text]

  • Jehanzeb H. Chaudhry, Eric C. Cyr, K. Liu, Thomas A. Manteuffel, Luke N. Olson, L. Tang. Enhancing Least-Squares Finite Element Methods Through a Quantity-of-Interest. SIAM Journal on Numerical Analysis (2014) [Text]

  • Jehanzeb H. Chaudhry, Jeffrey Comer, Aleksei Aksimentiev, Luke N. Olson. A Stabilized Finite Element Method for Modified Poisson–Nernst–Planck Equations to Determine Ion Flow Through a Nanopore. Communications in Computational Physics (2014) [Text]

  • Jehanzeb H. Chaudhry, Stephen D. Bond, Luke N. Olson. A Weighted Adaptive Least-Squares Finite Element Method for the Poisson–Boltzmann Equation. Applied Mathematics and Computation (2012) [Text]

  • Jehanzeb H. Chaudhry, Stephen D. Bond, Luke N. Olson. Finite Element Approximation to a Finite-Size Modified Poisson–Boltzmann Equation. Journal of Scientific Computing (2011) [Text]

  • Stephen D. Bond, Jehanzeb H. Chaudhry, Eric C. Cyr, Luke N. Olson. A First-Order System Least-Squares Finite Element Method for the Poisson–Boltzmann Equation. Journal of Computational Chemistry (2010) [Text]

Lattice Boltzmann Methods

  • Michael W. Brown, Jehanzeb H. Chaudhry, John N. Shadid. A Weighted Upwind Vector Kinetic Lattice Boltzmann Method for Hyperbolic Conservation Laws. [Preprint]

Collaborators:

Partial list of current and past collaborators:

  • Christopher D. Cooper. (Universidad Tecnica Federico Santa Maria, Chile)
  • Nishant Panda. (Los Alamos)
  • Joseph Bishop. (Sandia National Laboratories)
  • John Shadid. (Sandia National Laboratories)
  • Don Estep. (Simon Fraser University)
  • Simon Tavener. (Colorado State University)
  • Luke Olson. (University of Illinois at Urbana-Champaign)
  • Max Gunzburger
  • Eric Cyr. (Sandia National Laboratories)
  • Tim Wildey. (Sandia National Laboratories)