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On output functionals of boundary value problems on stochastic domains
Author(s) -
Harbrecht Helmut
Publication year - 2009
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1153
Subject(s) - mathematics , boundary value problem , domain (mathematical analysis) , perturbation (astronomy) , mathematical analysis , boundary (topology) , bellman equation , computation , function (biology) , fixed point , mathematical optimization , physics , algorithm , quantum mechanics , evolutionary biology , biology
We consider the computation of output functionals of random solutions to elliptic boundary value problems in domains with random boundary perturbations. We use a second‐order shape calculus to linearize the problem around a fixed nominal domain. For known mean and two‐point correlation function of the boundary perturbation, we derive, with leading order, deterministic expressions for the mean and the variance of the random output functional. These expressions include the solution of the boundary value problem on the nominal domain and a further, deterministic solution of the so‐called adjoint equation. The theoretical findings are supported and quantified by numerical experiments. Copyright © 2009 John Wiley & Sons, Ltd.