@article{1af2c719e3db4fa8b72727ab998e51ae,

title = "A Posteriori Error Analysis of Stochastic Differential Equations Using Polynomial Chaos Expansions",

abstract = "We develop computable a posteriori error estimates for linear functionals of a solution to a general nonlinear stochastic differential equation with random model/source parameters. These error estimates are based on a variational analysis applied to stochastic Galerkin methods for forward and adjoint problems. The result is a representation for the error estimate as a polynomial in the random model/source parameter. The advantage of this method is that we use polynomial chaos representations for the forward and adjoint systems to cheaply produce error estimates by simple evaluation of a polynomial. By comparison, the typical method of producing such estimates requires repeated forward/adjoint solves for each new choice of random parameter. We present numerical examples showing that there is excellent agreement between these methods. {\textcopyright} 2011 Society for Industrial and Applied Mathematics.",

author = "T. Butler and C. Dawson and T. Wildey",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: Submitted to the journal's Methods and Algorithms for Scientific Computing section May 18, 2010; accepted for publication (in revised form) March 2, 2011; published electronically June 7, 2011. This work was made possible with funding from the King Abdullah University of Science and Technology (KAUST).Sandia National Labs, Albuquerque, NM 87185 (tmwilde@sandia.gov). Sandia is a multiprogram laboratory operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94-AL85000. This author's work was partially supported by NSF grant DMS 0618679. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

year = "2011",

month = jan,

doi = "10.1137/100795760",

language = "English (US)",

volume = "33",

pages = "1267--1291",

journal = "SIAM Journal on Scientific Computing",

issn = "1064-8275",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "3",

}