A posteriori error analysis of a fully-mixed formulation for the Brinkman–Darcy problem
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| Autores: | , , |
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| Formato: | artículo original |
| Fecha de Publicación: | 2017 |
| Descripción: | We develop the a posteriori error analysis for a mixed finite element method applied to the coupling of Brinkman and Darcy equations in 3D, modelling the interaction of viscous and non-viscous flow effects across a given interface. The system is formulated in terms of velocity and pressure within the Darcy subdomain, together with vorticity, velocity and pressure of the fluid in the Brinkman region, and a Lagrange multiplier enforcing pressure continuity across the interface. The solvability of a fullymixed formulation along with a priori error bounds for a finite element method have been recently established in Álvarez et al. ( Comput Methods Appl Mech Eng 307:68– 95, 2016). Here we derive a residual-based a posteriori error estimator for such a scheme, and prove its reliability exploiting a global inf-sup condition in combination with suitable Helmholtz decompositions, and interpolation properties of Clément and Raviart–Thomas operators. The estimator is also shown to be efficient, following a localisation strategy and appropriate inverse inequalities. We present numerical tests to confirm the features of the estimator and to illustrate the performance of the method in academic and application-oriented problems. |
| País: | Kérwá |
| Institución: | Universidad de Costa Rica |
| Repositorio: | Kérwá |
| Lenguaje: | Inglés |
| OAI Identifier: | oai:kerwa.ucr.ac.cr:10669/87598 |
| Acceso en línea: | https://link.springer.com/article/10.1007/s10092-017-0238-z https://hdl.handle.net/10669/87598 |
| Palabra clave: | Brinkman–Darcy equations Vorticity-based formulation Mixed finite element methods A posteriori error analysis MATEMÁTICAS |