An augmented mixed–primal finite element method for a coupled flow–transport problem
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| Autores: | , , |
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| Formato: | artículo original |
| Fecha de Publicación: | 2015 |
| Descripción: | In 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. |
| País: | Kérwá |
| Institución: | Universidad de Costa Rica |
| Repositorio: | Kérwá |
| Lenguaje: | Inglés |
| OAI Identifier: | oai:kerwa.ucr.ac.cr:10669/87599 |
| Acceso en línea: | https://www.esaim-m2an.org/articles/m2an/abs/2015/05/m2an141070/m2an141070.html https://hdl.handle.net/10669/87599 |
| Palabra clave: | Stokes equations Nonlinear transport problem Augmented mixed-primal formulation Fixed point theory Thermal convection Sedimentation-consolidation process Finite element methods A priori error analysis MATEMÁTICAS |