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

Handle URI:
http://hdl.handle.net/10754/599662
Title:
Solution verification, goal-oriented adaptive methods for stochastic advection–diffusion problems
Authors:
Almeida, Regina C.; Oden, J. Tinsley
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.
Citation:
Almeida RC, Oden JT (2010) Solution verification, goal-oriented adaptive methods for stochastic advection–diffusion problems. Computer Methods in Applied Mechanics and Engineering 199: 2472–2486. Available: http://dx.doi.org/10.1016/j.cma.2010.04.001.
Publisher:
Elsevier BV
Journal:
Computer Methods in Applied Mechanics and Engineering
Issue Date:
Aug-2010
DOI:
10.1016/j.cma.2010.04.001
Type:
Article
ISSN:
0045-7825
Sponsors:
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.
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Full metadata record

DC FieldValue Language
dc.contributor.authorAlmeida, Regina C.en
dc.contributor.authorOden, J. Tinsleyen
dc.date.accessioned2016-02-28T06:06:58Zen
dc.date.available2016-02-28T06:06:58Zen
dc.date.issued2010-08en
dc.identifier.citationAlmeida RC, Oden JT (2010) Solution verification, goal-oriented adaptive methods for stochastic advection–diffusion problems. Computer Methods in Applied Mechanics and Engineering 199: 2472–2486. Available: http://dx.doi.org/10.1016/j.cma.2010.04.001.en
dc.identifier.issn0045-7825en
dc.identifier.doi10.1016/j.cma.2010.04.001en
dc.identifier.urihttp://hdl.handle.net/10754/599662en
dc.description.abstractA 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.en
dc.description.sponsorshipThis 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.en
dc.publisherElsevier BVen
dc.subjectGoal-oriented adaptivityen
dc.subjectStochastic advection-diffusion equationsen
dc.subjectStochastic collocation methoden
dc.titleSolution verification, goal-oriented adaptive methods for stochastic advection–diffusion problemsen
dc.typeArticleen
dc.identifier.journalComputer Methods in Applied Mechanics and Engineeringen
dc.contributor.institutionLaboratório Nacional de Computação Científica/MCT, ,en
dc.contributor.institutionUniversity of Texas at Austin, Austin, United Statesen
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