FULLY-DISCRETE FINITE ELEMENT APPROXIMATIONS FOR A FOURTH-ORDER LINEAR STOCHASTIC PARABOLIC EQUATION WITH ADDITIVE SPACE-TIME WHITE NOISE

被引：15
|
作者：
Kossioris, Georgios T. [1 ]
Zouraris, Georgios E.
机构：
[1] Univ Crete, Dept Math, Iraklion 71409, Crete, Greece
来源：
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS | 2010年 / 44卷 / 02期
关键词：
Finite element method; space-time white noise; Backward Euler time-stepping; fully-discrete approximations; a priori error estimates; DISCRETIZATION;
D O I：
10.1051/m2an/2010003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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 C-0 or C-1 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.
引用
收藏
页码：289 / 322
页数：34
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