Error analysis for the finite element approximation of the Brinkmann-Darcy-Forchheimer model for porous media with mixed boundary conditions
| Autor: | Pierre-Henri Cocquet, Delphine Ramalingom, Alain Bastide, Michaël Rakotobe |
|---|---|
| Přispěvatelé: | Physique et Ingénierie Mathématique pour l'Énergie, l'environnemeNt et le bâtimenT (PIMENT), Université de La Réunion (UR), ONERA - The French Aerospace Lab [Toulouse], ONERA |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Traction (engineering)
Porous media 010103 numerical & computational mathematics [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] 01 natural sciences Dirichlet distribution Physics::Fluid Dynamics symbols.namesake Finite element Convergence (routing) Applied mathematics Boundary value problem [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph] 0101 mathematics Mixed boundary conditions Mathematics Applied Mathematics Darcy-Brinkman-Forchheimer model Mixed boundary condition 16. Peace & justice Finite element method 010101 applied mathematics Computational Mathematics symbols Porous medium [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] Interpolation |
| Zdroj: | Journal of Computational and Applied Mathematics Journal of Computational and Applied Mathematics, Elsevier, 2020, ⟨10.1016/j.cam.2020.113008⟩ |
| ISSN: | 0377-0427 |
| DOI: | 10.1016/j.cam.2020.113008⟩ |
| Popis: | International audience; This paper deals with the finite element approximation of the Darcy-Brinkman-Forchheimer equation, involving a porous media with spatially-varying porosity, with mixed boundary condition such as inhomogeneous Dirichlet and traction boundary conditions. We first prove that the considered problem has a unique solution if the source terms are small enough. The convergence of a Taylor-Hood finite element approximation using a finite element interpolation of the porosity is then proved under similar smallness assumptions. Some optimal error estimates are next obtained when assuming the solution to the Darcy-Brinkman-Forchheimer model are smooth enough. We end this paper by providing a fixed-point method to solve iteratively the discrete non-linear problems and with some numerical experiments to make more precise the smallness assumptions on the source terms and to illustrate the theoretical convergence results. |
| Databáze: | OpenAIRE |
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