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Numerical solution of the Poisson equation on domains with a thin layer of random thickness

Dambrine, Marc and Greff, Isabelle and Harbrecht, Helmut and Puig, Benedicte. (2016) Numerical solution of the Poisson equation on domains with a thin layer of random thickness. SIAM journal on numerical analysis, 54 (2). pp. 921-941.

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Official URL: http://edoc.unibas.ch/42302/

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Abstract

The present article is dedicated to the numerical solution of the Poisson equation on domains with a thin layer of different conductivity and of random thickness. By changing the boundary condition, the boundary value problem given on a random domain is transformed into a boundary value problem on a fixed domain. The randomness is then contained in the coefficients of the new boundary condition. This thin coating can be expressed by a random Robin boundary condition which yields a third order accurate solution in the scale parameter ε of the layer’s thickness. With the help of the Karhunen–Loeve expansion, we transform this random boundary value problem into a deterministic parametric one with a possibly high-dimensional parameter y. Based on the decay of the random fluctuations of the layer’s thickness, we prove rates of decay of the derivatives of the random solution with respect to this parameter y which are robust in the scale parameter ε. Numerical results validate our theoretical findings.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
UniBasel Contributors:Harbrecht, Helmut
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Society for Industrial and Applied Mathematics
ISSN:1095-7170
Note:Publication type according to Uni Basel Research Database: Journal article
Language:English
Identification Number:
Last Modified:30 Jun 2016 11:03
Deposited On:04 Apr 2016 13:50

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