A High-Order HDG Method with Dubiner Basis for Elliptic Flow Problems

  1. Bastidas, Manuela 1
  2. Lopez-Rodríguez, Bibiana 2
  3. Osorio, Mauricio 2
  1. 1 University of Hasselt
    info

    University of Hasselt

    Hasselt, Bélgica

    ROR https://ror.org/04nbhqj75

  2. 2 Universidad Nacional de Colombia
    info

    Universidad Nacional de Colombia

    Bogotá, Colombia

    ROR https://ror.org/059yx9a68

Revista:
Ingeniería y ciencia

ISSN: 1794-9165

Año de publicación: 2020

Volumen: 16

Número: 32

Páginas: 33-54

Tipo: Artículo

DOI: 10.17230/INGCIENCIA.16.32.2 DIALNET GOOGLE SCHOLAR lock_openDialnet editor

Otras publicaciones en: Ingeniería y ciencia

Objetivos de desarrollo sostenible

Resumen

We propose a standard hybridizable discontinuous Galerkin (HDG) method to solve a classic problem in fluids mechanics: Darcy’s law. This model describes the behavior of a fluid trough a porous medium and it is relevant to the flow patterns on the macro scale. Here we present the theoretical results of existence and uniqueness of the weak and discontinuous solution of the second order elliptic equation, as well as the predicted convergence order of the HDG method. We highlight the use and implementation of Dubiner polynomial basis functions that allow us to develop a general and efficient high order numerical approximation. We also show some numerical examples that validate the theoretical results.

Referencias bibliográficas

  • Hybridizable discontinuous Galerkin methods, flow in porous media, Dubiner’s basis, high order convergence
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