Full Discretization of Stochastic Burgers Equation with Correlated Noise

  • The main purpose of this paper is to investigate the spectral Galerkin method for spatial discretization. We combine it with the method introduced by Kloeden, Jentzen & Winkel for temporal discretization of stochastic partial differential equations and study pathwise convergence. We consider the case of colored noise, instead of the usual space-time white noise that was used before for the spatial discretization. The rate of convergence in uniform topology is estimated for the stochastic Burgers equation. Numerical examples illustrate the estimated convergence rate.

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Metadaten
Author:Dirk BlömkerORCiDGND, Minoo Kamrani, Seyed Mohammad Hosseini
URN:urn:nbn:de:bvb:384-opus4-12780
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/1820
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2012-04)
Type:Preprint
Language:English
Year of first Publication:2012
Publishing Institution:Universität Augsburg
Release Date:2012/03/29
Tag:stochastische Konvolution; Diskretisierung
stochastic Burgers equation; colored noise
GND-Keyword:Burgers-Gleichung; Stochastische partielle Differentialgleichung; Stochastische parabolische Differentialgleichung; Galerkin-Methode; Farbiges Rauschen
Note:
Erschienen in IMA Journal of Numerical Analysis, 33, 3, S. 825-848, https://doi.org/10.1093/imanum/drs035
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):Deutsches Urheberrecht mit Print on Demand