7 papers · 1 filter
On Computing Coercivity Constants in Linear Variational Problems Through Eigenvalue Analysis
Peter Sentz, Jehanzeb Hameed Chaudhry, Luke N. Olson
In this work, we investigate the convergence of numerical approximations to coercivity constants of variational problems. These constants are essential components of rigorous error…
Efficient mesh refinement for the Poisson-Boltzmann equation with boundary elements
Vicente Ramm, Jehanzeb H. Chaudhry, Christopher D. Cooper
The Poisson-Boltzmann equation is a widely used model to study the electrostatics in molecular solvation. Its numerical solution using a boundary integral formulation requires a me…
An a posteriori error analysis for the equations of stationary incompressible magnetohydrodynamics
J. H. Chaudhry, A. E. Rappaport, J. N. Shadid
Magnetohydrodynamics (MHD) is a continuum level model for conducting fluids subject to external magnetic fields, e.g. plasmas and liquid metals. The efficient and robust solution o…
A Least-Squares Finite Element Reduced Basis Method
Jehanzeb Hameed Chaudhry, Luke N. Olson, Peter Sentz
We present a reduced basis (RB) method for parametrized linear elliptic partial differential equations (PDEs) in a least-squares finite element framework. A rigorous and reliable e…
A posteriori Error Estimation for the Spectral Deferred Correction Method
Jehanzeb H. Chaudhry, J. B. Collins
The spectral deferred correction method is a variant of the deferred correction method for solving ordinary differential equations. A benefit of this method is that is uses low ord…
Error estimation and uncertainty quantification for first time to a threshold value
Jehanzeb H. Chaudhry, Donald Estep, Zachary Stevens +1
Classical a posteriori error analysis for differential equations quantifies the error in a Quantity of Interest (QoI) which is represented as a bounded linear functional of the sol…