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

被引：0
作者：
Mihály Kovács
Stig Larsson
Fredrik Lindgren
机构：
[1] University of Otago,Department of Mathematics and Statistics
[2] Chalmers University of Technology and University of Gothenburg,Department of Mathematical Sciences
来源：
BIT Numerical Mathematics | 2012年 / 52卷
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; 65M60; 60H15; 60H35; 65C30;
D O I：
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中图分类号：
学科分类号：
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.
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页码：85 / 108
页数：23
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