Adaptive computation driven by an augmented fully-mixed FEM for double-diffusive natural convection in porous media
Gorde:
| Egileak: | , , |
|---|---|
| Argitaratze data: | 2026 |
| Deskribapena: | This work extends a previous study of ours, established in [M. Álvarez et al., Comput. Math. Appl., 114(2021), 112–131], on a semi-augmented mixed finite element formulation for doublediffusive natural convection in porous media, by developing and analyzing a new augmented fully mixed scheme in both two and three spatial dimensions. The formulation introduces a tensorial pseudo-thermosolutal gradient, depending on the gradients of temperature and concentration, as an additional unknown. This enrichment leads to a mixed system for the coupled equations and brings several computational advantages: the gradients of temperature and concentration can be efficiently recovered from the discrete solution without loss of accuracy; Dirichlet boundary conditions are incorporated naturally, without the need for Lagrange multipliers or extension operators; and the incorporation of parameterized redundant Galerkin terms ensures coercivity and allows the application of the Lax-Milgram theorem, thereby removing the need for inf-sup compatibility conditions and enabling greater flexibility in the selection of finite element subspaces. The scheme admits finite element spaces of arbitrary polynomial degree and achieves optimalorder convergence rates, established through both a priori and a posteriori error analyses. We also propose two computable residual-based a posteriori error estimators, which are entirely local and avoid the nonlocal norms required in previous approaches. These theoretical results are further supported by adaptive numerical experiments in two dimensions, which confirm the efficiency and reliability of the method. |
| Herria: | Kérwá |
| Erakundea: | Universidad de Costa Rica |
| Repositorio: | Kérwá |
| Hizkuntza: | Inglés |
| OAI Identifier: | oai:kerwa.ucr.ac.cr:10669/105140 |
| Sarrera elektronikoa: | https://hdl.handle.net/10669/105140 https://doi.org/10.1016/j.jcp.2026.114711 |
| Gako-hitza: | Double-diffusive natural convection Oberbeck-Boussinesq model Augmented formulation Fully-mixed finite element method Fixed point theory A priori error analysis A posteriori error analysis Numerical analysis Equations Mathematical models |