An augmented mixed–primal finite element method for a coupled flow–transport problem

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dc.creatorÁlvarez Guadamuz, Mario Andrés
dc.creatorGatica Pérez, Gabriel Nibaldo
dc.creatorRuiz Baier, Ricardo
dc.date.accessioned2022-11-04T16:32:22Z
dc.date.available2022-11-04T16:32:22Z
dc.date.issued2015
dc.description.abstractIn this paper we analyze the coupling of a scalar nonlinear convection-diffusion problem with the Stokes equations where the viscosity depends on the distribution of the solution to the transport problem. An augmented variational approach for the fluid flow coupled with a primal formulation for the transport model is proposed. The resulting Galerkin scheme yields an augmented mixed-primal finite element method employing Raviart−Thomas spaces of order k for the Cauchy stress, and continuous piecewise polynomials of degree ≤ k + 1 for the velocity and also for the scalar field. The classical Schauder and Brouwer fixed point theorems are utilized to establish existence of solution of the con- tinuous and discrete formulations, respectively. In turn, suitable estimates arising from the connection between a regularity assumption and the Sobolev embedding and Rellich−Kondrachov compactness theorems, are also employed in the continuous analysis. Then, sufficiently small data allow us to prove uniqueness and to derive optimal a priori error estimates. Finally, we report a few numerical tests confirming the predicted rates of convergence, and illustrating the performance of a linearized method based on Newton−Raphson iterations; and we apply the proposed framework in the simulation of thermal convection and sedimentation-consolidation processes.es_ES
dc.description.procedenceUCR::Sedes Regionales::Sede de Occidentees_ES
dc.description.procedenceUCR::Vicerrectoría de Docencia::Ciencias Básicas::Facultad de Ciencias::Escuela de Matemáticaes_ES
dc.description.sponsorshipUniversidad de Concepciónes_ES
dc.description.sponsorshipUniversidad de Chilees_ES
dc.description.sponsorshipSwiss National Science Foundationes_ES
dc.identifier.citationhttps://www.esaim-m2an.org/articles/m2an/abs/2015/05/m2an141070/m2an141070.htmles_ES
dc.identifier.doi10.1051/m2an/2015015
dc.identifier.issn1399-1427
dc.identifier.urihttps://hdl.handle.net/10669/87599
dc.language.isoenges_ES
dc.rightsacceso embargado
dc.sourceMathematical Modelling and Numerical Analysis, 49(5), p. 1399 - 1427.es_ES
dc.subjectStokes equationses_ES
dc.subjectNonlinear transport problemes_ES
dc.subjectAugmented mixed-primal formulationes_ES
dc.subjectFixed point theoryes_ES
dc.subjectThermal convectiones_ES
dc.subjectSedimentation-consolidation processes_ES
dc.subjectFinite element methodses_ES
dc.subjectA priori error analysises_ES
dc.subjectMATEMÁTICASes_ES
dc.titleAn augmented mixed–primal finite element method for a coupled flow–transport problemes_ES
dc.typeartículo originales_ES

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M. Álvarez et al. An augmented mixed-primal finite element method for a coupled flow-transport problem. Mathematical Modelling and Numerical Analysis, (2015).pdf
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M. Álvarez, G.N. Gatica and R. Ruiz-Baier. An augmented mixed–primal finite element method for a coupled flow–transport problem. ESAIM: Mathematical Modelling and Numerical Analysis, vol. 49, 5, pp. 1399-1427, (2015).
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