Weak convergence of finite element approximations of linear stochastic evolution equations with additive noise
Journal article, 2012

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.

Finite element

Parabolic equation

Hyperbolic equation

Wiener process

Error estimate

Wave equation


Weak convergence

Heat equation

Additive noise

Cahn-Hilliard-Cook equation


Mihaly Kovacs

University of Otago

Stig Larsson

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Fredrik Lindgren

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

BIT (Copenhagen)

0006-3835 (ISSN)

Vol. 52 1 85-108

Subject Categories

Computational Mathematics


Basic sciences



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