Adaptive Uncertainty Quantification for Stochastic Hyperbolic Conservation Laws
We propose a predictor-corrector adaptive method for the study of hyperbolic partial
differential equations (PDEs) under uncertainty. Constructed around the framework of …
differential equations (PDEs) under uncertainty. Constructed around the framework of …
Adjoint-based Adaptive Multi-Level Monte Carlo for Differential Equations
J Chaudhry, Z Stevens - arXiv preprint arXiv:2206.02905, 2022 - arxiv.org
We present a multi-level Monte Carlo (MLMC) algorithm with adaptively refined meshes and
accurately computed stopping-criteria utilizing adjoint-based a posteriori error analysis for …
accurately computed stopping-criteria utilizing adjoint-based a posteriori error analysis for …
Error estimation for the time to a threshold value in evolutionary partial differential equations
JH Chaudhry, D Estep, T Giannini, Z Stevens… - BIT Numerical …, 2023 - Springer
We develop an a posteriori error analysis for a numerical estimate of the time at which a
functional of the solution to a partial differential equation (PDE) first achieves a threshold …
functional of the solution to a partial differential equation (PDE) first achieves a threshold …
Robust Uncertainty Quantification With Analysis of Error in Standard and Non-Standard Quantities of Interest
Z Stevens - 2022 - search.proquest.com
This thesis derives two Uncertainty Quantification (UQ) methods for differential equations
that depend on random parameters:(i) error bounds for a computed cumulative distribution …
that depend on random parameters:(i) error bounds for a computed cumulative distribution …