On solving elliptic stochastic partial differential equations

A model elliptic boundary value problem of second order, with stochastic coefficients described by the Karhunen–Loève expansion is addressed. This problem is transformed into an equivalent deterministic one. The perturbation method and the method of successive approximations is analyzed. Rigorous er...

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Veröffentlicht in:	Computer methods in applied mechanics and engineering 2002-08, Vol.191 (37), p.4093-4122
Hauptverfasser:	Babuška, Ivo, Chatzipantelidis, Panagiotis
Format:	Artikel
Sprache:	eng
Schlagworte:	Exact sciences and technology Karhunen–Loève expansion Mathematical methods in physics Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical approximation and analysis Numerical solution of partial differential equations Ordinary and partial differential equations, boundary value problems Partial differential equations, initial value problems and time-dependant initial-boundary value problems Physics Sciences and techniques of general use Stochastic partial differential equations Successive approximations
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Beschreibung
Zusammenfassung:	A model elliptic boundary value problem of second order, with stochastic coefficients described by the Karhunen–Loève expansion is addressed. This problem is transformed into an equivalent deterministic one. The perturbation method and the method of successive approximations is analyzed. Rigorous error estimates in the framework of Sobolev spaces are given.
ISSN:	0045-7825 1879-2138
DOI:	10.1016/S0045-7825(02)00354-7