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Combination technique based second moment analysis for elliptic PDEs on random domains

Harbrecht, Helmut and Peters, Michael. (2016) Combination technique based second moment analysis for elliptic PDEs on random domains. In: Sparse grids and applications - Stuttgart 2014. Switzerland, pp. 51-77.

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Abstract

In this article, we propose the sparse grid combination technique for the second moment analysis of elliptic partial differential equations on random domains. By employing shape sensitivity analysis, we linearize the influence of the random domain perturbation on the solution. We derive deterministic partial differential equations to approximate the random solution’s mean and its covariance with leading order in the amplitude of the random domain perturbation. The partial differential equation for the covariance is a tensor product Dirichlet problem which can efficiently be determined by Galerkin’s method in the sparse tensor product space. We show that this Galerkin approximation coincides with the solution derived from the combination technique if the detail spaces in the related multiscale hierarchy are constructed with respect to Galerkin projections. This means that the combination technique does not impose an additional error in our construction. Numerical experiments quantify and qualify the proposed method.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
UniBasel Contributors:Harbrecht, Helmut and Peters, Michael
Item Type:Book Section, refereed
Book Section Subtype:Further Contribution in a Book
Publisher:Springer International Publishing
ISBN:978-3-319-28262-6
Series Name:Lecture notes in computational science and engineering
Issue Number:109
Note:Publication type according to Uni Basel Research Database: Book item -- The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-28262-6_3
Language:English
Identification Number:
Last Modified:16 Aug 2017 13:24
Deposited On:04 Apr 2016 12:59

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