Generalities on finite element discretization for fractional pressure diffusion equation in the fractal continuum

Authors

  • H. D. Sánchez Chávez Departamento de Física, Universidad Tecnológica de la Mixteca Km. 2.5 Carretera a Acatlima, Huajuapan de León, Oaxaca, 69000, México.
  • C. A. López-Ortiz Departamento de Física, Universidad Tecnológica de la Mixteca Km. 2.5 Carretera a Acatlima, Huajuapan de León, Oaxaca, 69000, México.
  • and L. Flores-Cano Departamento de Física, Universidad Tecnológica de la Mixteca Km. 2.5 Carretera a Acatlima, Huajuapan de León, Oaxaca, 69000, México.

DOI:

https://doi.org/10.31349/RevMexFis.65.251

Keywords:

Finite Element, Fractional Calculus in Fractal Continuum, Anisotropic Continous Fractal Flow, Fractional Pressure Diffusion Equation, Continuum Mechanics.

Abstract

In this study we explore the application of the novel fractional calculus in fractal continuum (FCFC), together with the finite element method (FEM), in order to analize explicitly how these differential operators act in the process of discretizing the generalized fractional pressure diffusion equation for a three-dimensional anisotropic continuous fractal flow. The master finite element equation (MFEE) for arbitrary interpolation functions is obtained. As an example, MFEE for the case of a generic linear tetrahedron in $\mathbb{R}^3$ is shown. Analytic solution for the spatial variables is determined over a canonical tetrahedral finite element in global coordinates.

Downloads

Published

2019-05-07

How to Cite

[1]
H. D. Sánchez Chávez, C. A. López-Ortiz, and and L. Flores-Cano, “Generalities on finite element discretization for fractional pressure diffusion equation in the fractal continuum”, Rev. Mex. Fís., vol. 65, no. 3 May-Jun, pp. 251–260, May 2019.

Issue

Vol. 65 No. 3 May-Jun (2019): Revista Mexicana de Física

Section

06 Fluid Dynamics

License

Authors retain copyright and grant the Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.