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Pré-Publication, Document De Travail Année : 2007

Neumann conditions on fractal boundaries

Yves Achdou
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Résumé

We consider some elliptic boundary value problems in a self-similar ramified domain of ℝ2 with a fractal boundary with Laplace's equation and nonhomogeneous Neumann boundary conditions. The Hausdorff dimension of the fractal boundary is greater than one. The goal is twofold: first rigorously define the boundary value problems, second approximate the restriction of the solutions to subdomains obtained by stopping the geometric construction after a finite number of steps. For the first task, a key step is the definition of a trace operator. For the second task, a multiscale strategy based on transparent boundary conditions and on a wavelet expansion of the Neumann datum is proposed, following an idea contained in a previous work by the same authors. Error estimates are given and numerical results are presented.
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Dates et versions

hal-00139849 , version 1 (03-04-2007)

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  • HAL Id : hal-00139849 , version 1

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Yves Achdou, Nicoletta Tchou. Neumann conditions on fractal boundaries. 2007. ⟨hal-00139849⟩
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