Int. J. Numer. Anal. Mod., 11 (2014), pp. 288-302.


A subgrid viscosity Lagrange-Galerkin method for convection-diffusion problems

Rodolfo Bermejo 1, Pedro Galán Del Sastre 2, Laura Saavedra 3

1 Departamento deMatemática Aplicada ETSII, Universidad Politécnica deMadrid, José Gutérrez Abascal, 2 28006 Madrid, Spain
2 Departamento deMatemática Aplicada ETSA, Universidad Politécnica de Madrid, Avda. Juan de Herrera, 2 28040 Madrid, Spain
3 Departamento de Fundamentos Matemáticos ETSIA, Universidad Politécnica de Madrid, Plaza del Cardenal Cisneros, 2 28040 Madrid, Spain

Received by the editors October 29, 2012 and, in revised form, April 8, 2013

Abstract

We present and analyze a subgrid viscosity Lagrange-Galerkin method that combines the subgrid eddy viscosity method proposed in W. Layton, A connection between subgrid scale eddy viscosity and mixed methods. Appl. Math. Comp., 133: 147-157, 2002, and a conventional Lagrange-Galerkin method in the framework of P_1⊕ cubic bubble finite elements. This results in an efficient and easy to implement stabilized method for convection dominated convection diffusion- reaction problems. Numerical experiments support the numerical analysis results and show that the new method is more accurate than the conventional Lagrange-Galerkin one.

AMS subject classifications: 65M12, 65M25, 65M60
Key words: Subgrid viscosity, Lagrange-Galerkin, finite elements, convection-diffusion-reaction problems.

Email: rbermejo@etsii.upm.es, pedro.galan@upm.es, laura.saavedra@upm.es
 

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