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Electronic Transactions on Numerical Analysis.

Volume 34, pp. 170-186, 2009.

Copyright2009, Kent State University.

ISSN 1068-9613.

ETNA

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

ON THE DISCRETE SOLUTION OF THE GENERALIZED STOKES PROBLEM IN ONE TIME-STEP FOR TWO PHASE FLOW

WILFREDO ANGULOyANDHILDA L ´OPEZz

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

Abstract. In this paper, we demonstrate the existence, uniqueness, and uniform stability of the discrete solution obtained with the nonconforming Crouzeix-Raviart/P0 finite element for a generalized Stokes problem of a two- phase flow in one time-step.

Key words. two-phase flow, Stokes problem, discrete solution, finite element AMS subject classifications. 15A15, 15A09, 15A23

Received March 31, 2008. Accepted May 5, 2009. Published online on December 29, 2009. Recommended by Godela Scherer. This paper was supported by the bilateral agreement France-Venezuela, ECOSNORD-FONACIT and Consejo de Desarrollo Cient´ıfico y Human´ıstico.

ySchool of Science, Universidad Centroccidental “Lisandro Alvarado”, Barquisimeto, Venezuela and Post- graduate degree in Mathematics, Faculty of Science, Universidad Central de Venezuela, Caracas, Venezuela ([email protected]).

zCenter for Scientific and Technological Calculations, Faculty of Science, Universidad Central de Venezuela, Caracas, Venezuela ([email protected]).

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