Diffusion and propagation problems in some ramified domains with a fractal boundary

DOI10.1051/m2an:2006027zbMath1112.65115OpenAlexW2096131668MaRDI QIDQ3418632

Yves Achdou, Christophe Sabot, Nicoletta Tchou

Publication date: 5 February 2007

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=M2AN_2006__40_4_623_0

zbMATH Keywords

Laplace equationHelmholtz equationPoisson equationelliptic boundary value problemsNeumann and transparent boundary conditions

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items

Density and trace results in generalized fractal networks, Transparent boundary conditions for the Helmholtz equation in some ramified domains with a fractal boundary, Explicit formulas for homogenization limits in certain non‐periodic problems including ramified domains, Finite difference and finite element methods for partial differential equations on fractals, Well-Posed PDE and Integral Equation Formulations for Scattering by Fractal Screens, Trace results on domains with self-similar fractal boundaries, Uniform weighted estimates on pre-fractal domains, Long-term behavior of reaction-diffusion equations with nonlocal boundary conditions on rough domains, Transparent boundary conditions for a class of boundary value problems in some ramified domains with a fractal boundary, Wave propagation in fractal trees. Mathematical and numerical issues, Homogenization of Heat Diffusion in a Cracked Medium, Traces on General Sets in ${R}^n$ for Functions with no Differentiability Requirements

Cites Work

• Transparent boundary conditions for the Helmholtz equation in some ramified domains with a fractal boundary
• Exact non-reflecting boundary conditions
• Quasiconformal mappings and extendability of functions in Sobolev spaces
• A transmission problem with a fractal interface.
• Spectral properties of self-similar lattices and iteration of rational maps
• Sampling on the Sierpinski Gasket
• A Multiscale Numerical Method for Poisson Problems in Some Ramified Domains with a Fractal Boundary
• The finite element method on the Sierpinski gasket
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