Solution verification, goal-oriented adaptive methods for stochastic advection–diffusion problems

Regina C. Almeida; J. Tinsley Oden

doi:10.1016/j.cma.2010.04.001

Solution verification, goal-oriented adaptive methods for stochastic advection–diffusion problems

Regina C. Almeida, J. Tinsley Oden

Research output: Contribution to journal › Article › peer-review

29 Scopus citations

Abstract

A goal-oriented analysis of linear, stochastic advection-diffusion models is presented which provides both a method for solution verification as well as a basis for improving results through adaptation of both the mesh and the way random variables are approximated. A class of model problems with random coefficients and source terms is cast in a variational setting. Specific quantities of interest are specified which are also random variables. A stochastic adjoint problem associated with the quantities of interest is formulated and a posteriori error estimates are derived. These are used to guide an adaptive algorithm which adjusts the sparse probabilistic grid so as to control the approximation error. Numerical examples are given to demonstrate the methodology for a specific model problem. © 2010 Elsevier B.V.

Original language	English (US)
Pages (from-to)	2472-2486
Number of pages	15
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	199
Issue number	37-40
DOIs	https://doi.org/10.1016/j.cma.2010.04.001
State	Published - Aug 2010
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This research is partially supported by the Brazilian Government, through the Agency CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior), under grant # 0858/08-0. The first author also would like to acknowledge the support of the J.T. Oden Faculty Fellowship Research Program at ICES. The support of the work of JTO under DOE contract DE-FC52-08NA28615 in connection with the Predictive Science Academic Alliance Program is gratefully acknowledged. Additionally, support of JTO under research grant KAUST U.S. Limited: US 00003 is gratefully acknowledged.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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10.1016/j.cma.2010.04.001

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title = "Solution verification, goal-oriented adaptive methods for stochastic advection–diffusion problems",

abstract = "A goal-oriented analysis of linear, stochastic advection-diffusion models is presented which provides both a method for solution verification as well as a basis for improving results through adaptation of both the mesh and the way random variables are approximated. A class of model problems with random coefficients and source terms is cast in a variational setting. Specific quantities of interest are specified which are also random variables. A stochastic adjoint problem associated with the quantities of interest is formulated and a posteriori error estimates are derived. These are used to guide an adaptive algorithm which adjusts the sparse probabilistic grid so as to control the approximation error. Numerical examples are given to demonstrate the methodology for a specific model problem. {\textcopyright} 2010 Elsevier B.V.",

author = "Almeida, {Regina C.} and Oden, {J. Tinsley}",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: This research is partially supported by the Brazilian Government, through the Agency CAPES (Coordena{\c c}{\~a}o de Aperfei{\c c}oamento de Pessoal de N{\'i}vel Superior), under grant # 0858/08-0. The first author also would like to acknowledge the support of the J.T. Oden Faculty Fellowship Research Program at ICES. The support of the work of JTO under DOE contract DE-FC52-08NA28615 in connection with the Predictive Science Academic Alliance Program is gratefully acknowledged. Additionally, support of JTO under research grant KAUST U.S. Limited: US 00003 is gratefully acknowledged. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

year = "2010",

month = aug,

doi = "10.1016/j.cma.2010.04.001",

language = "English (US)",

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N2 - A goal-oriented analysis of linear, stochastic advection-diffusion models is presented which provides both a method for solution verification as well as a basis for improving results through adaptation of both the mesh and the way random variables are approximated. A class of model problems with random coefficients and source terms is cast in a variational setting. Specific quantities of interest are specified which are also random variables. A stochastic adjoint problem associated with the quantities of interest is formulated and a posteriori error estimates are derived. These are used to guide an adaptive algorithm which adjusts the sparse probabilistic grid so as to control the approximation error. Numerical examples are given to demonstrate the methodology for a specific model problem. © 2010 Elsevier B.V.

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ER -

Solution verification, goal-oriented adaptive methods for stochastic advection–diffusion problems

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