TY - JOUR
T1 - Solution verification, goal-oriented adaptive methods for stochastic advection–diffusion problems
AU - Almeida, Regina C.
AU - Oden, J. Tinsley
N1 - 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.
PY - 2010/8
Y1 - 2010/8
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.
AB - 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.
UR - http://hdl.handle.net/10754/599662
UR - https://linkinghub.elsevier.com/retrieve/pii/S0045782510001180
UR - http://www.scopus.com/inward/record.url?scp=77954757412&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2010.04.001
DO - 10.1016/j.cma.2010.04.001
M3 - Article
SN - 0045-7825
VL - 199
SP - 2472
EP - 2486
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
IS - 37-40
ER -