Weak formulation of Hadamard variation applied to the filtration problem

  • Takashi Suzuki
  • Takuya TsuchiyaEmail author
Original Paper Area 2


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.


Hadamard variation Filtration problem 

Mathematics Subject Classification (2000)

35J05 35R35 


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Copyright information

© The JJIAM Publishing Committee and Springer 2011

Authors and Affiliations

  1. 1.Division of Mathematical Science, Department of System Innovation, Graduate School of Engineering ScienceOsaka UniversityToyonakaJapan
  2. 2.Graduate School of Science and EngineeringEhime UniversityMatsuyamaJapan

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