Semidiscrete Galerkin Approximation for a Linear Stochastic Parabolic Partial Differential Equation Driven by an Additive Noise期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Semidiscrete Galerkin Approximation for a Linear Stochastic Parabolic Partial Differential Equation Driven by an Additive Noise

Authors:	Yubin?Yan author-information" > author-information__contact u-icon-before" > mailto:yubin@maths.man.ac.uk" title=" yubin@maths.man.ac.uk" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author

Affiliation:	(1) Department of Mathematics, The University of Manchester, Manchester, M13 9PL, England

Abstract:	We study the semidiscrete Galerkin approximation of a stochastic parabolic partial differential equation forced by an additive space-time noise. The discretization in space is done by a piecewise linear finite element method. The space-time noise is approximated by using the generalized L₂ projection operator. Optimal strong convergence error estimates in the L₂ and $dot{H}^{-1}$ norms with respect to the spatial variable are obtained. The proof is based on appropriate nonsmooth data error estimates for the corresponding deterministic parabolic problem. The error estimates are applicable in the multi-dimensional case.AMS subject classification (2000) 65M, 60H15, 65C30, 65M65.Received April 2004. Revised September 2004. Communicated by Anders Szepessy.

Keywords:	stochastic parabolic partial differential equations finite element method additive noise Hilbert space
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