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The second order perturbation approach for elliptic partial differential equations on random domains

Harbrecht, Helmut and Peters, Michael D.. (2018) The second order perturbation approach for elliptic partial differential equations on random domains. Applied Numerical Mathematics, 125. pp. 159-171.

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Abstract

The present article is dedicated to the solution of elliptic boundary value problems on random domains. We apply a high-precision second order shape Taylor expansion to quantify the impact of the random perturbation on the solution. Thus, we obtain a representation of the solution with third order accuracy in the size of the perturbation's amplitude. The major advantage of this approach is that we end up with purely deterministic equations for the solution's moments. In particular, we derive representations for the first four moments, i.e., expectation, variance, skewness and kurtosis. These moments are efficiently computable by means of boundary integral equations. Numerical results are presented to validate the presented approach.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
UniBasel Contributors:Harbrecht, Helmut and Peters, Michael
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Elsevier
ISSN:0168-9274
Note:Publication type according to Uni Basel Research Database: Journal article
Language:English
Identification Number:
Last Modified:28 Dec 2017 10:47
Deposited On:28 Dec 2017 10:47

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