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IMA Journal of Numerical Analysis 2004 24(4):605-634; doi:10.1093/imanum/24.4.605
© 2004 by Institute of Mathematics and its Applications
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Mixed finite element approximation for the stochastic pressure equation of Wick type

Hassan Manouzi1 and Thomas Gorm Theting2

1 Departement de Mathématiques et Statistique, Université Laval, Quebec, G1K7P4, Canada 2 Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway

We propose a mixed finite element method for the numerical solution of the stochastic pressure equation of Wick type. In this formulation, the pressure and the velocity are the most relevant unknowns. We give existence and uniqueness results for the continuous problem and its approximation. Optimal error estimates are derived and algorithmic aspects are discussed. Finally, the results of numerical experiments confirm the practical efficiency of the mixed method.

Key Words: finite element method; flow in porous media; stochastic partial differential equations; stochastic simulation; Wick product

Received 14 April 2003. Revised 19 October 2003.


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