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

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.

• Autores: Bastidas, Manuela; Lopez-Rodríguez, Bibiana; Osorio, Mauricio
• Fecha de publicación: 2020
• Institución: Universidad EAFIT
• Repositorio: Repositorio EAFIT
• Idioma: eng
• OAI Identifier: oai:repository.eafit.edu.co:10784/25804
• Acceso en línea: http://hdl.handle.net/10784/25804
• Palabra clave: Hybridizable discontinuous Galerkin methods; flow in porous media; Dubiner’s basis; high order convergence; Método de Galerkin discontinuo hibridizable; flujo en medioporoso; bases de Dubiner; convergencia de alto orden
• Rights: openAccess
• License: Copyright © 2020 Manuela Bastidas, Bibiana Lopez-Rodríguez, Mauricio Osorio