• Corpus ID: 246210124

Finite difference and finite element methods for partial differential equations on fractals

@article{Contreras2022FiniteDA,
  title={Finite difference and finite element methods for partial differential equations on fractals},
  author={Fernando R. L. Contreras and Juan Galvis},
  journal={ArXiv},
  year={2022},
  volume={abs/2201.08433}
}
In this paper, we present numerical procedures to compute solutions of partial differential equations posed on fractals. In particular, we consider the strong form of the equation using standard graph Laplacian matrices and also weak forms of the equation derived using standard length or area measure on a discrete approximation of the fractal set. We then introduce a numerical procedure to normalize the obtained diffusions, that is, a way to compute the renormalization constant needed in the de… 

References

SHOWING 1-10 OF 12 REFERENCES
The finite element method on the Sierpinski gasket, Constructive approximation, Springer-Verlag New York
  • 2001
Reaction and Diffusion on the Sierpinski Gasket
In this thesis we study non-linear dynamical systems on complex domains. Although the systems we consider are mathematical abstractions, our motivation is to gain insights into neurobiological
Diffusion and propagation problems in some ramified domains with a fractal boundary
This paper is devoted to some elliptic boundary value problems in a self-similar ramified domain of with a fractal boundary. Both the Laplace and Helmholtz equations are studied. A generalized
Partial differential equations with numerical methods
TLDR
A Two-Point Boundary Value Problem with Finite Difference Methods for Elliptic Equations and Finite Element methods for Hyperbolic Equations.
Análise em fractais, coloquio Brasileiro de matemáticas
  • Instituto Nacional de Matemática Pura e Aplicada (Impa),
  • 2013
Analysis on fractal
    Differential equations on fractal, a tutorial, Priceton university
    • 2006
    The finite element method on the Sierpinski gasket, Constructive approximation
    • 2001
    Differential equations on fractal, a tutorial
    • 2006
    Christophe Sabot , Nicoletta Tchou , Diffusion and propagation problem in some ramified domains with a fractal boundary
    • 2006
    ...
    ...