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A Review of Recent Developments in the Numerical Solution of Stochastic Partial Differential Equations (Stochastic Finite Elements). - (Informatikbericht ; Nr. 2003-6)

Autor/en :

Keese, Andreas

Institut / Verlag :

Institut für Wissenschaftliches Rechnen, 2003

Fakultät :

01 - Mathematik und Informatik

Freigeschaltet am :

31.01.2012

Dokumente :

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Umfang :

117 S.

Sprache :

englisch

Kurzfassung :

The present review discusses recent developments in numerical techniques for the solution of systems with stochastic uncertainties. Such systems are modelled by stochastic partial differential equations (SPDEs), and techniques for their discretisation by stochastic finite elements (SFEM) are reviewed. Also, short overviews of related fields are given, e.g. of mathematical properties of random fields and SPDEs and of techniques for high-dimensional integration. After a summary of aspects of stochastic analysis, models and representations of random variables are presented. Then mathematical theories for SPDEs with stochastic operator are reviewed. Discretisation-techniques for random fields and for SPDEs are summarised and solvers for the resulting discretisations are reviewed, where the main focus lies on series expansions in the stochastic dimensions with an emphasis on Galerkin-schemes.

Schlagwörter :

Stochastische Finite Elemente

Sachgebiet :

004 Datenverarbeitung; Informatik

Typ :

Publikationen der TU Braunschweig

Format :

Text/Dokument

URN:NBN :

urn:nbn:de:gbv:084-12013115384

Zitierfähige URL :

http://www.digibib.tu-bs.de/?docid=00001504