Fast and reliable methods for determining the evolution of uncertain parameters in differential equations

DOI10.1016/j.jcp.2005.08.024zbMath1089.65058OpenAlexW2093668144MaRDI QIDQ2489699

D. Neckels, Donald J. Estep

Publication date: 28 April 2006

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2005.08.024

zbMATH Keywords

numerical examplesFinite element methodSensitivity analysisMonte-Carlo methodA posteriori error estimationUncertainty quantificationAdaptive samplingStochastic systemVariational analysisAdaptive error controlGeneralized Green's functionParameter errorParameter variationReliable sampling

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Numerical computation of solutions to systems of equations (65H10) Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Error bounds for numerical methods for ordinary differential equations (65L70)

Related Items (6)

A method for solving stochastic equations by reduced order models and local approximations ⋮ Automatic simplification of systems of reaction-diffusion equations by \textit{a posteriori} analysis ⋮ Goal-oriented adaptive surrogate construction for stochastic inversion ⋮ Fast and reliable methods for determining the evolution of uncertain parameters in differential equations ⋮ Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities ⋮ Fast methods for determining the evolution of uncertain parameters in reaction-diffusion equations

Uses Software

• QSHEP3D

Cites Work

• Mathematical statistics. An introduction
• Fast and reliable methods for determining the evolution of uncertain parameters in differential equations
• Multivariate interpolation of large sets of scattered data
• THE POINTWISE COMPUTABILITY OF THE LORENZ SYSTEM
• A Posteriori Error Bounds and Global Error Control for Approximation of Ordinary Differential Equations
• Estimating the error of numerical solutions of systems of reaction-diffusion equations
• Generalized Green's Functions and the Effective Domain of Influence
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