Fully-discrete finite element approximations for a fourth-order linear stochastic parabolic equation with additive space-time white noise

Georgios T. Kossioris; Georgios E. Zouraris

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 44, Issue: 2, page 289-322
  • ISSN: 0764-583X

Abstract

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We consider an initial and Dirichlet boundary value problem for a fourth-order linear stochastic parabolic equation, in one space dimension, forced by an additive space-time white noise. Discretizing the space-time white noise a modelling error is introduced and a regularized fourth-order linear stochastic parabolic problem is obtained. Fully-discrete approximations to the solution of the regularized problem are constructed by using, for discretization in space, a Galerkin finite element method based on C0 or C1 piecewise polynomials, and, for time-stepping, the Backward Euler method. We derive strong a priori estimates for the modelling error and for the approximation error to the solution of the regularized problem.

How to cite

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Kossioris, Georgios T., and Zouraris, Georgios E.. "Fully-discrete finite element approximations for a fourth-order linear stochastic parabolic equation with additive space-time white noise." ESAIM: Mathematical Modelling and Numerical Analysis 44.2 (2010): 289-322. <http://eudml.org/doc/250856>.

@article{Kossioris2010,
abstract = { We consider an initial and Dirichlet boundary value problem for a fourth-order linear stochastic parabolic equation, in one space dimension, forced by an additive space-time white noise. Discretizing the space-time white noise a modelling error is introduced and a regularized fourth-order linear stochastic parabolic problem is obtained. Fully-discrete approximations to the solution of the regularized problem are constructed by using, for discretization in space, a Galerkin finite element method based on C0 or C1 piecewise polynomials, and, for time-stepping, the Backward Euler method. We derive strong a priori estimates for the modelling error and for the approximation error to the solution of the regularized problem. },
author = {Kossioris, Georgios T., Zouraris, Georgios E.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Finite element method; space-time white noise; Backward Euler time-stepping; fully-discrete approximations; a priori error estimates; finite element method; backward Euler time-stepping; initial-boundary value problem; fourth-order linear stochastic parabolic equation},
language = {eng},
month = {3},
number = {2},
pages = {289-322},
publisher = {EDP Sciences},
title = {Fully-discrete finite element approximations for a fourth-order linear stochastic parabolic equation with additive space-time white noise},
url = {http://eudml.org/doc/250856},
volume = {44},
year = {2010},
}

TY - JOUR
AU - Kossioris, Georgios T.
AU - Zouraris, Georgios E.
TI - Fully-discrete finite element approximations for a fourth-order linear stochastic parabolic equation with additive space-time white noise
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 44
IS - 2
SP - 289
EP - 322
AB - We consider an initial and Dirichlet boundary value problem for a fourth-order linear stochastic parabolic equation, in one space dimension, forced by an additive space-time white noise. Discretizing the space-time white noise a modelling error is introduced and a regularized fourth-order linear stochastic parabolic problem is obtained. Fully-discrete approximations to the solution of the regularized problem are constructed by using, for discretization in space, a Galerkin finite element method based on C0 or C1 piecewise polynomials, and, for time-stepping, the Backward Euler method. We derive strong a priori estimates for the modelling error and for the approximation error to the solution of the regularized problem.
LA - eng
KW - Finite element method; space-time white noise; Backward Euler time-stepping; fully-discrete approximations; a priori error estimates; finite element method; backward Euler time-stepping; initial-boundary value problem; fourth-order linear stochastic parabolic equation
UR - http://eudml.org/doc/250856
ER -

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