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A mixed-primal finite element method for the coupling of Brinkman-Darcy flow and nonlinear transport.
dc.creator | Álvarez Guadamuz, Mario Andrés | |
dc.creator | Gatica Pérez, Gabriel Nibaldo | |
dc.creator | Ruiz Baier, Ricardo | |
dc.date.accessioned | 2022-11-04T16:21:12Z | |
dc.date.available | 2022-11-04T16:21:12Z | |
dc.date.issued | 2021-01 | |
dc.identifier.citation | https://academic.oup.com/imajna/article-abstract/41/1/381/5771306?redirectedFrom=fulltext | es_ES |
dc.identifier.issn | 1464-3642 | |
dc.identifier.issn | 0272-4979 | |
dc.identifier.uri | https://hdl.handle.net/10669/87596 | |
dc.description.abstract | This paper is devoted to the mathematical and numerical analysis of a model describing the interfacial flow-transport interaction in a porous-fluidic domain. The medium consists of a highly permeable material, where the flow of an incompressible viscous fluid is governed by Brinkman equations (written in terms of vorticity, velocity and pressure), and a porous medium where Darcy’s law describes fluid motion using filtration velocity and pressure. Gravity and the local fluctuations of a scalar field (representing for instance, the solids volume fraction or the concentration of a contaminant) are the main drivers of the fluid patterns on the whole domain, and the Brinkman-Darcy equations are coupled to a nonlinear transport equation accounting for mass balance of the scalar concentration. We introduce a mixedprimal variational formulation of the problem and establish existence and uniqueness of solution using fixed-point arguments and small-data assumptions. A family of Galerkin discretizations that produce divergence-free discrete velocities is also presented and analysed using similar tools to those employed in the continuous problem. Convergence of the resulting mixed-primal finite element method is proven, and some numerical examples confirming the theoretical error bounds and illustrating the performance of the proposed discrete scheme are reported. | es_ES |
dc.description.sponsorship | Universidad de Costa Rica/[540-B7-233]/UCR/Costa Rica | es_ES |
dc.description.sponsorship | Comisión Nacional de Investigación Científica y Tecnológica/[AFB170001]/CONICYT/Chile | es_ES |
dc.description.sponsorship | Engineering and Physical Sciences Research Council/[Research Grant EP/R00207X/1]/EPSRC/Reino Unido | es_ES |
dc.language.iso | eng | es_ES |
dc.source | IMA Journal of Numerical Analysis, vol. 41(1), pp. 381-411 | es_ES |
dc.subject | Nonlinear transport | es_ES |
dc.subject | Brinkman–Darcy coupling | es_ES |
dc.subject | Vorticity-based formulation | es_ES |
dc.subject | Fixed-point theory | es_ES |
dc.subject | Mixed finite elements | es_ES |
dc.subject | Error Analysis | es_ES |
dc.subject | MATEMÁTICAS | es_ES |
dc.title | A mixed-primal finite element method for the coupling of Brinkman-Darcy flow and nonlinear transport. | es_ES |
dc.type | artículo original | es_ES |
dc.identifier.doi | 10.1093/imanum/drz060 | |
dc.description.procedence | UCR::Sedes Regionales::Sede de Occidente | es_ES |
dc.description.procedence | UCR::Vicerrectoría de Docencia::Ciencias Básicas::Facultad de Ciencias::Escuela de Matemática | es_ES |
dc.identifier.codproyecto | 540-B7-233 |
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