Weak convergence of finite element approximations of linear stochastic evolution equations with additive noise

被引：50

作者：

Kovacs, Mihaly ^{[3
]}

Larsson, Stig ^{[1
,2
]}

Lindgren, Fredrik ^{[1
,2
]}

机构：

[1] Chalmers, Dept Math Sci, S-41296 Gothenburg, Sweden

[2] Univ Gothenburg, S-41296 Gothenburg, Sweden

[3] Univ Otago, Dept Math & Stat, Dunedin, New Zealand

来源：

BIT NUMERICAL MATHEMATICS | 2012年 / 52卷 / 01期

基金：

瑞典研究理事会;

关键词：

Finite element; Parabolic equation; Hyperbolic equation; Stochastic; Heat equation; Cahn-Hilliard-Cook equation; Wave equation; Additive noise; Wiener process; Error estimate; Weak convergence; WAVE-EQUATION; HEAT-EQUATION; ORDER;

D O I：

10.1007/s10543-011-0344-2

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

A unified approach is given for the analysis of the weak error of spatially semidiscrete finite element methods for linear stochastic partial differential equations driven by additive noise. An error representation formula is found in an abstract setting based on the semigroup formulation of stochastic evolution equations. This is then applied to the stochastic heat, linearized Cahn-Hilliard, and wave equations. In all cases it is found that the rate of weak convergence is twice the rate of strong convergence, sometimes up to a logarithmic factor, under the same or, essentially the same, regularity requirements.

引用

页码：85 / 108

页数：24

共 15 条

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[2]

Da Prato G, 1992, STOCHASTIC EQUATIONS

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