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Analysis of an augmented mixed-FEM for the Navier-Stokes problem

Opened Access Analysis of an augmented mixed-FEM for the Navier-Stokes problem

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Autor: Camaño Valenzuela, Jessika
Oyarzúa Vargas, Ricardo
Tierra Chica, Giordano
Departamento: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Fecha: 2016
Publicado en: Mathematics of Computation
Tipo de documento: Artículo
Resumen: In this paper we propose and analyze a new augmented mixed finite element method for the Navier-Stokes problem. Our approach is based on the introduction of a “nonlinearpseudostress” tensor linking the pseudostress tensor with the convective term, which leads to a mixed formulation with the nonlinear-pseudostress tensor and the velocity as the main unknowns of the system. Further variables of interest, such as the fluid pressure, the fluid vorticity and the fluid velocity gradient, can be easily approximated as a simple postprocess of the finite element solutions with the same rate of convergence. The resulting mixed formulation is augmented by introducing Galerkin least-squares type terms arising from the constitutive and equilibrium equations of the Navier-Stokes equations and from the Dirichlet boundary condition, which are multiplied by stabilization parameters that are chosen in such a way that the resulting continuous formulation becomes well-posed. Then, the classical Banach’...
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Cita: Camaño Valenzuela, J., Oyarzúa Vargas, R. y Tierra Chica, G. (2016). Analysis of an augmented mixed-FEM for the Navier-Stokes problem. Mathematics of Computation
Tamaño: 1.151Mb
Formato: PDF

URI: http://hdl.handle.net/11441/42632

DOI: http://dx.doi.org/10.1090/mcom/3124

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