Weak convergence of finite element approximations of linear stochastic evolution equations with additive noise
Artikel i vetenskaplig tidskrift, 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

Stochastic

Weak convergence

Heat equation

Additive noise

Cahn-Hilliard-Cook equation

Författare

Mihaly Kovacs

University of Otago

Stig Larsson

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Fredrik Lindgren

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

BIT (Copenhagen)

0006-3835 (ISSN)

Vol. 52 1 85-108

Ämneskategorier

Beräkningsmatematik

Fundament

Grundläggande vetenskaper

DOI

10.1007/s10543-011-0344-2

Mer information

Skapat

2017-10-06