Journal
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS
Volume 28, Issue 2, Pages 327-350Publisher
KINOKUNIYA CO LTD
DOI: 10.1007/s13160-011-0044-y
Keywords
Hadamard variation; Filtration problem
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Funding
- Japan Society for the Promotion of Science [22540139]
- Grants-in-Aid for Scientific Research [22540139, 23340023] Funding Source: KAKEN
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Quantities defined using a solution of an elliptic boundary value problem may vary when the boundary of the domain is perturbed. Such a variation with respect to domain perturbation is called Hadamard variation. We present a weak formulation of Hadamard variation and apply it to the filtration (or dam) problem. We obtain first Hadamard variations of quantities arising in the variational principle of the filtration problem. The correctness of the obtained first variations is confirmed by numerical experiments. Using the first variations, we propose a numerical iterative scheme for the filtration problem. Numerical examples show good performance of the presented scheme.
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