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

Almeida, Regina C.; Oden, J. Tinsley

doi:10.1016/j.cma.2010.04.001

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

Journal Article · Sun Aug 01 04:00:00 EDT 2010 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2010.04.001· OSTI ID:1092062

Almeida, Regina C. ^[1]; Oden, J. Tinsley

University of Texas at Austin, Institute for Computational Engineering and Sciences

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.

Research Organization:: Univ. of Texas, Austin, TX (United States)

Sponsoring Organization:: USDOE SC Office of Advanced Scientific Computing Research (SC-21)

DOE Contract Number:: FG02-05ER25701

OSTI ID:: 1092062

Report Number(s):: DOE/ER-25701

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Journal Issue: 37-40 Vol. 199; ISSN 0045-7825

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

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