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Electronic Transactions on Numerical Analysis.

Volume 34, pp. 187-203, 2009.

Copyright2009, Kent State University.

ISSN 1068-9613.

ETNA

Kent State University http://etna.math.kent.edu

COMPARISON BETWEEN DIFFERENT NUMERICAL DISCRETIZATIONS FOR A DARCY-FORCHHEIMER MODEL

HILDA L ´OPEZy, BR´ıGIDA MOLINAy,ANDJOS ´E J. SALASz

Dedicated to V´ıctor Pereyra on the occasion of his 70th birthday

Abstract. This paper is a numerical study of different discretizations for a mixed formulation of the Darcy- Forchheimer equation. Different finite elements are used: constant functions, conformal linear functions and Crouzeix- Raviart non-conformal finite elements. The behavior of the discretizations is analyzed through a comparative study of some test problems. The numerical results suggest that one of the proposed discretizations has better convergence properties for the velocity.

Key words. Darcy-Forchheimer’s model, mixed formulation, numerical discretizations, finite elements, algo- rithm of alternating directions.

AMS subject classifications. 35Q35, 74S05, 58C15, 65F10

Received June 5, 2008. Accepted May 25, 2009. Published online on December 29, 2009. Recommended by Godela Scherer. This paper was supported by the Consejo de Desarrollo Cient´ıfico y Human´ıstico of the Universidad Central de Venezuela.

yCentro de C´alculo Cient´ıfico y Tecnol´ogico, Escuela de Computaci´on, Universidad Central de Venezuela, Cara- cas, Venezuela.fhlopez,bmolinag@kuaimare.ciens.ucv.ve.

zDepartamento de Educaci´on F´ısica y Matem´aticas, Universidad Cat´olica Andr´es Bello, Caracas, Venezuela.

[email protected].

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