Efficient Distribution Estimation and Uncertainty Quantification for Elliptic Problems on Domains with Stochastic Boundaries

We study the problem of uncertainty quantification for the numerical solution of elliptic partial differential equation boundary value problems posed on domains with stochastically varying boundaries. We also use the uncertainty quantification results to tackle the efficient solution of such problem...

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Bibliographic Details
Published in:arXiv.org 2018-07
Main Authors: Chaudhry, Jehanzeb H, Burch, Nathanial, Estep, Donald
Format: Article
Language:English
Subjects:
Boundaries
Boundary value problems
Domains
Error analysis
Partial differential equations
Transformations (mathematics)
Uncertainty
Online Access:Get full text
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Summary:We study the problem of uncertainty quantification for the numerical solution of elliptic partial differential equation boundary value problems posed on domains with stochastically varying boundaries. We also use the uncertainty quantification results to tackle the efficient solution of such problems. We introduce simple transformations that map a family of domains with stochastic boundaries to a fixed reference domain. We exploit the transformations to carry out a prior and a posteriori error analyses and to derive an efficient Monte Carlo sampling procedure.
ISSN:2331-8422