Analytical approximation and numerical studies of one-dimensional elliptic equation with random coefficients
- Authors:
- Publication Date:
- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- OSTI Identifier:
- 1616766
- Alternate Identifier(s):
- OSTI ID: 1426025
- Grant/Contract Number:
- AC05-76RL01830
- Resource Type:
- Published Article
- Journal Name:
- Applied Mathematical Modelling
- Additional Journal Information:
- Journal Name: Applied Mathematical Modelling Journal Volume: 40 Journal Issue: 9-10; Journal ID: ISSN 0307-904X
- Publisher:
- Elsevier
- Country of Publication:
- United Kingdom
- Language:
- English
Citation Formats
Xu, Zhijie, Tipireddy, Ramakrishna, and Lin, Guang. Analytical approximation and numerical studies of one-dimensional elliptic equation with random coefficients. United Kingdom: N. p., 2016.
Web. doi:10.1016/j.apm.2015.12.041.
Xu, Zhijie, Tipireddy, Ramakrishna, & Lin, Guang. Analytical approximation and numerical studies of one-dimensional elliptic equation with random coefficients. United Kingdom. https://doi.org/10.1016/j.apm.2015.12.041
Xu, Zhijie, Tipireddy, Ramakrishna, and Lin, Guang. Sun .
"Analytical approximation and numerical studies of one-dimensional elliptic equation with random coefficients". United Kingdom. https://doi.org/10.1016/j.apm.2015.12.041.
@article{osti_1616766,
title = {Analytical approximation and numerical studies of one-dimensional elliptic equation with random coefficients},
author = {Xu, Zhijie and Tipireddy, Ramakrishna and Lin, Guang},
abstractNote = {},
doi = {10.1016/j.apm.2015.12.041},
journal = {Applied Mathematical Modelling},
number = 9-10,
volume = 40,
place = {United Kingdom},
year = {Sun May 01 00:00:00 EDT 2016},
month = {Sun May 01 00:00:00 EDT 2016}
}
Free Publicly Available Full Text
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https://doi.org/10.1016/j.apm.2015.12.041
https://doi.org/10.1016/j.apm.2015.12.041
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Cited by: 8 works
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Works referenced in this record:
Numerical Studies of Three-dimensional Stochastic Darcy’s Equation and Stochastic Advection-Diffusion-Dispersion Equation
journal, January 2010
- Lin, G.; Tartakovsky, A. M.
- Journal of Scientific Computing, Vol. 43, Issue 1
High-Order Collocation Methods for Differential Equations with Random Inputs
journal, January 2005
- Xiu, Dongbin; Hesthaven, Jan S.
- SIAM Journal on Scientific Computing, Vol. 27, Issue 3
An efficient, high-order probabilistic collocation method on sparse grids for three-dimensional flow and solute transport in randomly heterogeneous porous media
journal, May 2009
- Lin, G.; Tartakovsky, A. M.
- Advances in Water Resources, Vol. 32, Issue 5
Upscaling of solute transport in heterogeneous media with non-uniform flow and dispersion fields
journal, October 2013
- Xu, Zhijie; Meakin, Paul
- Applied Mathematical Modelling, Vol. 37, Issue 18-19
On the ratio of two correlated normal random variables
journal, January 1969
- Hinkley, D. V.
- Biometrika, Vol. 56, Issue 3
Uncertainty quantification via random domain decomposition and probabilistic collocation on sparse grids
journal, September 2010
- Lin, G.; Tartakovsky, A. M.; Tartakovsky, D. M.
- Journal of Computational Physics, Vol. 229, Issue 19
Random Airy type differential equations: Mean square exact and numerical solutions
journal, September 2010
- Cortés, J. -C.; Jódar, L.; Camacho, F.
- Computers & Mathematics with Applications, Vol. 60, Issue 5
Selection of polynomial chaos bases via Bayesian model uncertainty methods with applications to sparse approximation of PDEs with stochastic inputs
journal, February 2014
- Karagiannis, Georgios; Lin, Guang
- Journal of Computational Physics, Vol. 259
Probabilistic models for stochastic elliptic partial differential equations
journal, November 2010
- Grigoriu, Mircea
- Journal of Computational Physics, Vol. 229, Issue 22
Numerical solution of spectral stochastic finite element systems
journal, January 1996
- Ghanem, Roger G.; Kruger, Robert M.
- Computer Methods in Applied Mechanics and Engineering, Vol. 129, Issue 3
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
journal, January 2007
- Babuška, Ivo; Nobile, Fabio; Tempone, Raúl
- SIAM Journal on Numerical Analysis, Vol. 45, Issue 3
A stochastic analysis of steady and transient heat conduction in random media using a homogenization approach
journal, July 2014
- Xu, Zhijie
- Applied Mathematical Modelling, Vol. 38, Issue 13
Iterative solution of systems of linear equations arising in the context of stochastic finite elements
journal, August 2000
- Pellissetti, M. F.; Ghanem, R. G.
- Advances in Engineering Software, Vol. 31, Issue 8-9
Computational aspects of the stochastic finite element method
journal, January 2007
- Eiermann, Michael; Ernst, Oliver G.; Ullmann, Elisabeth
- Computing and Visualization in Science, Vol. 10, Issue 1
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
journal, January 2002
- Xiu, Dongbin; Karniadakis, George Em
- SIAM Journal on Scientific Computing, Vol. 24, Issue 2
A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
journal, January 2008
- Nobile, F.; Tempone, R.; Webster, C. G.
- SIAM Journal on Numerical Analysis, Vol. 46, Issue 5
Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
journal, January 2004
- Babuska, Ivo; Tempone, Raúl; Zouraris, Georgios E.
- SIAM Journal on Numerical Analysis, Vol. 42, Issue 2
Basis adaptation in homogeneous chaos spaces
journal, February 2014
- Tipireddy, Ramakrishna; Ghanem, Roger
- Journal of Computational Physics, Vol. 259
Numerical and analytical solutions of new generalized fractional diffusion equation
journal, December 2013
- Xu, Yufeng; He, Zhimin; Agrawal, Om P.
- Computers & Mathematics with Applications, Vol. 66, Issue 10
Adaptive ANOVA decomposition of stochastic incompressible and compressible flows
journal, February 2012
- Yang, Xiu; Choi, Minseok; Lin, Guang
- Journal of Computational Physics, Vol. 231, Issue 4
Iterative Solvers for the Stochastic Finite Element Method
journal, January 2010
- Rosseel, Eveline; Vandewalle, Stefan
- SIAM Journal on Scientific Computing, Vol. 32, Issue 1