Analysis of a semi-augmented mixed finite element method for double-diffusive natural convection in porous media
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| Autores: | , , |
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| Formato: | artículo original |
| Fecha de Publicación: | 2022 |
| Descripción: | In this paper we study a stationary double-diffusive natural convection problem in porous media given by a Navier-Stokes/Brinkman type system, for describing the velocity and the pressure, coupled to a vector advection-diffusion equation relate to the heat and substance concentration, of a viscous fluid in a porous media with physical boundary conditions. The model problem is rewritten in terms of a first-order system, without the pressure, based on the introduction of the strain tensor and a nonlinear pseudo-stress tensor in the fluid equations. After a variational approach, the resulting weak model is then augmented using appropriate redundant penalization terms for the fluid equations along with a standard primal formulation for the heat and substance concentration. Then, it is rewritten as an equivalent fixed-point problem. Well-posedness results for both the continuous and the discrete schemes are stated, as well as the respective convergence result under certain regularity assumptions combined with the Lax-Milgram theorem, and the Banach and Brouwer fixed-point theorems. In particular, Raviart-Thomas elements of order k are used for approximating the pseudo-stress tensor, piecewise polynomials of degree ≤k and ≤k+1 are utilized for approximating the strain tensor and the velocity, respectively, and the heat and substance concentration are approximated by means of Lagrange finite elements of order ≤k+1. Optimal a priori error estimates are derived and confirmed through some numerical examples that illustrate the performance of the proposed semi-augmented mixed-primal scheme. |
| País: | Kérwá |
| Institución: | Universidad de Costa Rica |
| Repositorio: | Kérwá |
| Lenguaje: | Inglés |
| OAI Identifier: | oai:kerwa.ucr.ac.cr:10669/87544 |
| Acceso en línea: | https://www.sciencedirect.com/science/article/abs/pii/S0898122122001225?via%3Dihub#! https://hdl.handle.net/10669/87544 |
| Palabra clave: | Double-diffusive natural convection Oberbeck-Boussinesq model Augmented formulation Mixed-primal finite element method Fixed point theory A priori error analysis |