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A finite element approximation of linear stochastic PDEs driven by multiplicative white noise

Authors: H. Manouzi;

A finite element approximation of linear stochastic PDEs driven by multiplicative white noise

Abstract

In this paper we present a finite element approximation of linear stochastic PDEs driven by multiplicative white noise. Using the Wick-product properties and the Wiener-Ito chaos expansion, the stochastic variational problem is reformulated as a set of deterministic variational problems. To obtain the chaos coefficients in the corresponding deterministic equations, we use the usual Galerkin finite element method using standard techniques. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.

Related Organizations
Subjects by Vocabulary

Microsoft Academic Graph classification: Multiplicative white noise Finite element limit analysis Mathematical analysis Mixed finite element method White noise Finite element method Set (abstract data type) Galerkin finite element method Extended finite element method Mathematics

Keywords

Applied Mathematics, Computer Science Applications, Computational Theory and Mathematics

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  • citations
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    10
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
10
Average
Average
Average
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