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Solving Cauchy problems by minimizing an energy-like functional

Abstract : An energy-like error functional is introduced in the context of the ill-posed problem of boundary data recovering, which is well known as a Cauchy problem. Links with existing methods for data completion are detailed. Here the problem is converted into an optimization problem; the computation of the gradients of the energy-like functional is given for both the continuous and the discrete problems. Numerical experiments highlight the efficiency of the proposed method as well as its robustness in the model context of Laplace's equation, but also for anisotropic conductivity problems.
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https://hal.archives-ouvertes.fr/hal-00139569
Contributor : Thouraya Baranger <>
Submitted on : Monday, April 2, 2007 - 11:10:57 AM
Last modification on : Wednesday, October 28, 2020 - 12:10:04 PM

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  • HAL Id : hal-00139569, version 1

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Stéphane Andrieux, Thouraya Baranger, Amel Ben Abda. Solving Cauchy problems by minimizing an energy-like functional. Inverse Problems, IOP Publishing, 2006, 22, pp.115-133. ⟨hal-00139569⟩

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