Analytical approximation and numerical studies of one-dimensional elliptic equation with random coefficients

Xu, Zhijie; Tipireddy, Ramakrishna; Lin, Guang

doi:10.1016/j.apm.2015.12.041

Title: Analytical approximation and numerical studies of one-dimensional elliptic equation with random coefficients

Journal Article · Sun May 01 00:00:00 EDT 2016 · Applied Mathematical Modelling

DOI:https://doi.org/10.1016/j.apm.2015.12.041· OSTI ID:1616766

; Tipireddy, Ramakrishna; Lin, Guang

View Journal Article

Cite

Export

Save

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC05-76RL01830

OSTI ID:: 1616766

Alternate ID(s):: OSTI ID: 1426025

Journal Information:: Applied Mathematical Modelling, Journal Name: Applied Mathematical Modelling Vol. 40 Journal Issue: 9-10; ISSN 0307-904X

Publisher:: ElsevierCopyright Statement

Country of Publication:: United Kingdom

Language:: English

Citation Metrics:

Cited by: 8 works

Citation information provided by
Web of Science

References (21)

Numerical Studies of Three-dimensional Stochastic Darcy’s Equation and Stochastic Advection-Diffusion-Dispersion Equation Lin, G.; Tartakovsky, A. M. Journal of Scientific Computing, Vol. 43, Issue 1 https://doi.org/10.1007/s10915-010-9346-5	journal	January 2010
High-Order Collocation Methods for Differential Equations with Random Inputs Xiu, Dongbin; Hesthaven, Jan S. SIAM Journal on Scientific Computing, Vol. 27, Issue 3 https://doi.org/10.1137/040615201	journal	January 2005
An efficient, high-order probabilistic collocation method on sparse grids for three-dimensional flow and solute transport in randomly heterogeneous porous media Lin, G.; Tartakovsky, A. M. Advances in Water Resources, Vol. 32, Issue 5 https://doi.org/10.1016/j.advwatres.2008.09.003	journal	May 2009
Upscaling of solute transport in heterogeneous media with non-uniform flow and dispersion fields Xu, Zhijie; Meakin, Paul Applied Mathematical Modelling, Vol. 37, Issue 18-19 https://doi.org/10.1016/j.apm.2013.03.070	journal	October 2013
On the ratio of two correlated normal random variables Hinkley, D. V. Biometrika, Vol. 56, Issue 3 https://doi.org/10.1093/biomet/56.3.635	journal	January 1969
Uncertainty quantification via random domain decomposition and probabilistic collocation on sparse grids Lin, G.; Tartakovsky, A. M.; Tartakovsky, D. M. Journal of Computational Physics, Vol. 229, Issue 19 https://doi.org/10.1016/j.jcp.2010.05.036	journal	September 2010
Random Airy type differential equations: Mean square exact and numerical solutions Cortés, J. -C.; Jódar, L.; Camacho, F. Computers & Mathematics with Applications, Vol. 60, Issue 5 https://doi.org/10.1016/j.camwa.2010.05.046	journal	September 2010
Selection of polynomial chaos bases via Bayesian model uncertainty methods with applications to sparse approximation of PDEs with stochastic inputs Karagiannis, Georgios; Lin, Guang Journal of Computational Physics, Vol. 259 https://doi.org/10.1016/j.jcp.2013.11.016	journal	February 2014
Probabilistic models for stochastic elliptic partial differential equations Grigoriu, Mircea Journal of Computational Physics, Vol. 229, Issue 22 https://doi.org/10.1016/j.jcp.2010.07.023	journal	November 2010
Numerical solution of spectral stochastic finite element systems Ghanem, Roger G.; Kruger, Robert M. Computer Methods in Applied Mechanics and Engineering, Vol. 129, Issue 3 https://doi.org/10.1016/0045-7825(95)00909-4	journal	January 1996
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data Babuška, Ivo; Nobile, Fabio; Tempone, Raúl SIAM Journal on Numerical Analysis, Vol. 45, Issue 3 https://doi.org/10.1137/050645142	journal	January 2007
A stochastic analysis of steady and transient heat conduction in random media using a homogenization approach Xu, Zhijie Applied Mathematical Modelling, Vol. 38, Issue 13 https://doi.org/10.1016/j.apm.2013.11.044	journal	July 2014
Iterative solution of systems of linear equations arising in the context of stochastic finite elements Pellissetti, M. F.; Ghanem, R. G. Advances in Engineering Software, Vol. 31, Issue 8-9 https://doi.org/10.1016/S0965-9978(00)00034-X	journal	August 2000
Computational aspects of the stochastic finite element method Eiermann, Michael; Ernst, Oliver G.; Ullmann, Elisabeth Computing and Visualization in Science, Vol. 10, Issue 1 https://doi.org/10.1007/s00791-006-0047-4	journal	January 2007
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations Xiu, Dongbin; Karniadakis, George Em SIAM Journal on Scientific Computing, Vol. 24, Issue 2 https://doi.org/10.1137/S1064827501387826	journal	January 2002
A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data Nobile, F.; Tempone, R.; Webster, C. G. SIAM Journal on Numerical Analysis, Vol. 46, Issue 5 https://doi.org/10.1137/060663660	journal	January 2008
Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations Babuska, Ivo; Tempone, Raúl; Zouraris, Georgios E. SIAM Journal on Numerical Analysis, Vol. 42, Issue 2 https://doi.org/10.1137/S0036142902418680	journal	January 2004
Basis adaptation in homogeneous chaos spaces Tipireddy, Ramakrishna; Ghanem, Roger Journal of Computational Physics, Vol. 259 https://doi.org/10.1016/j.jcp.2013.12.009	journal	February 2014
Numerical and analytical solutions of new generalized fractional diffusion equation Xu, Yufeng; He, Zhimin; Agrawal, Om P. Computers & Mathematics with Applications, Vol. 66, Issue 10 https://doi.org/10.1016/j.camwa.2013.08.028	journal	December 2013
Adaptive ANOVA decomposition of stochastic incompressible and compressible flows Yang, Xiu; Choi, Minseok; Lin, Guang Journal of Computational Physics, Vol. 231, Issue 4 https://doi.org/10.1016/j.jcp.2011.10.028	journal	February 2012
Iterative Solvers for the Stochastic Finite Element Method Rosseel, Eveline; Vandewalle, Stefan SIAM Journal on Scientific Computing, Vol. 32, Issue 1 https://doi.org/10.1137/080727026	journal	January 2010

Similar Records

Analytical Approximation and Numerical Studies of One-dimensional Elliptic Equation with Random Coefficients

Journal Article · Fri Apr 01 00:00:00 EDT 2016 · Applied Mathematical Modelling · OSTI ID:1616766

Xu, Zhijie; Tipireddy, Ramakrishna; Lin, Guang

Analytical Approximation and Numerical Studies of One-dimensional Eliptic Equation with Random Coefficients

Journal Article · Sun May 01 00:00:00 EDT 2016 · Applied Mathematical Modelling · OSTI ID:1616766

Xu, Zhijie; Tipireddy, Ramakrishna; Lin, Guang

A two-level stochastic collocation method for semilinear elliptic equations with random coefficients

Journal Article · Mon May 01 00:00:00 EDT 2017 · Journal of Computational and Applied Mathematics · OSTI ID:1616766

Chen, Luoping; Zheng, Bin; Lin, Guang; +1 more

Title: Analytical approximation and numerical studies of one-dimensional elliptic equation with random coefficients

Citation Formats

References (21)

Similar Records

Related Subjects