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Göteborgs universitets publikationer

Weak convergence of finite element approximations of linear stochastic evolution equations with additive noise II. Fully discrete schemes

Författare och institution:
Mihaly Kovacs (-); Stig Larsson (Institutionen för matematiska vetenskaper, matematik, Chalmers/GU); Fredrik Lindgren (Institutionen för matematiska vetenskaper, matematik, Chalmers/GU)
Publicerad i:
BIT Numerical Mathematics, 53 ( 2 ) s. 497-525
Artikel, refereegranskad vetenskaplig
Fulltextlänk (lokalt arkiv):
Sammanfattning (abstract):
We present an abstract framework for analyzing the weak error of fully discrete approximation schemes for linear evolution equations driven by additive Gaussian noise. First, an abstract representation formula is derived for sufficiently smooth test functions. The formula is then applied to the wave equation, where the spatial approximation is done via the standard continuous finite element method and the time discretization via an I-stable rational approximation to the exponential function. It is found that the rate of weak convergence is twice that of strong convergence. Furthermore, in contrast to the parabolic case, higher order schemes in time, such as the Crank-Nicolson scheme, are worthwhile to use if the solution is not very regular. Finally we apply the theory to parabolic equations and detail a weak error estimate for the linearized Cahn-Hilliard-Cook equation as well as comment on the stochastic heat equation.
Länk till sammanfattning (abstract):
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
Matematik ->
Beräkningsmatematik ->
Tillämpad matematik ->
Numerisk analys
Chalmers fundament:
Grundläggande vetenskaper
Ytterligare information:
Received: 9 March 2012 / Accepted: 3 October 2012
Postens nummer:
Ingår i post nr:
Posten skapad:
2012-11-08 08:36
Posten ändrad:
2014-09-02 15:21

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