Доступ предоставлен для: Guest
Портал Begell Электронная Бибилиотека e-Книги Журналы Справочники и Сборники статей Коллекции
International Journal for Uncertainty Quantification
Импакт фактор: 3.259 5-летний Импакт фактор: 2.547 SJR: 0.417 SNIP: 0.8 CiteScore™: 1.52

ISSN Печать: 2152-5080
ISSN Онлайн: 2152-5099

Свободный доступ

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2014007972
pages 423-454

SOME A PRIORI ERROR ESTIMATES FOR FINITE ELEMENT APPROXIMATIONS OF ELLIPTIC AND PARABOLIC LINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

Christophe Audouze
University of Toronto Institute for Aerospace Studies, 4925 Dufferin Street, Ontario, Canada M3H 5T6
Prasanth B. Nair
University of Toronto Institute for Aerospace Studies, 4925 Dufferin Street, Ontario, Canada M3H 5T6

Краткое описание

We study some theoretical aspects of Legendre polynomial chaos based finite element approximations of elliptic and parabolic linear stochastic partial differential equations (SPDEs) and provide a priori error estimates in tensor product Sobolev spaces that hold under appropriate regularity assumptions. Our analysis takes place in the setting of finite-dimensional noise, where the SPDE coefficients depend on a finite number of second-order random variables. We first derive a priori error estimates for finite element approximations of a class of linear elliptic SPDEs. Subsequently, we consider finite element approximations of parabolic SPDEs coupled with a Θ-weighted temporal discretization scheme. We establish conditions under which the time-stepping scheme is stable and derive a priori rates of convergence as a function of spatial, temporal, and stochastic discretization parameters. We later consider steady-state and time-dependent stochastic diffusion equations and illustrate how the general results provided here can be applied to specific SPDE models. Finally, we theoretically analyze primal and adjoint-based recovery of stochastic linear output functionals that depend on the solution of elliptic SPDEs and show that these schemes are superconvergent.


Articles with similar content:

Sufficient Optimality Conditions for Control Problem of Random Structure Systems with Infinite Aftereffect under the Presence of Markovian Parameters
Journal of Automation and Information Sciences, Vol.41, 2009, issue 4
Victor I. Musurivskiy
On an Approach to Identification of Dynamic Systems Under Uncertainty
Journal of Automation and Information Sciences, Vol.32, 2000, issue 3
Vyacheslav F. Gubarev, Nikolay N. Aksenov
Minimax Estimation for Solutions of Transmissions Problems for Elliptic Equations under Absence of Information about Conjugating Conditions
Journal of Automation and Information Sciences, Vol.32, 2000, issue 12
Yuriy K. Podlipenko, Amer Mansor Dababneh
A PRIORI ERROR ANALYSIS OF STOCHASTIC GALERKIN PROJECTION SCHEMES FOR RANDOMLY PARAMETRIZED ORDINARY DIFFERENTIAL EQUATIONS
International Journal for Uncertainty Quantification, Vol.6, 2016, issue 4
Christophe Audouze , Prasanth B. Nair
ASSESSMENT OF COLLOCATION AND GALERKIN APPROACHES TO LINEAR DIFFUSION EQUATIONS WITH RANDOM DATA
International Journal for Uncertainty Quantification, Vol.1, 2011, issue 1
Raymond S. Tuminaro, Eric T. Phipps, Christopher W. Miller, Howard C. Elman