Articles | Volume 26, issue 20
Research article
19 Oct 2022
Research article |  | 19 Oct 2022

A robust upwind mixed hybrid finite element method for transport in variably saturated porous media

Anis Younes, Hussein Hoteit, Rainer Helmig, and Marwan Fahs

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Cited articles

Belfort, B., Ramasomanana, F., Younes, A., and Lehmann, F.: An Efficient Lumped Mixed Hybrid Finite Element Formulation for Variably Saturated Groundwater Flow, Vadose Zone J., 8, 352–362,, 2009. 
Brezzi, F. and Fortin, M. (Eds.): Mixed and Hybrid Finite Element Methods, Springer, New York, NY,, 1991. 
Brezzi, F., Douglas, J., and Marini, L. D.: Two families of mixed finite elements for second order elliptic problems, Numer. Math., 47, 217–235,, 1985. 
Brunner, F., Radu, F. A., and Knabner, P.: Analysis of an Upwind-Mixed Hybrid Finite Element Method for Transport Problems, SIAM J. Numer. Anal., 52, 83–102,, 2014. 
Chavent, G. and Jaffré, J.: Mathematical models and finite elements for reservoir simulation: single phase, multiphase, and multicomponent flows through porous media, North-Holland, Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co, Amsterdam, New York, NY, USA, 376 pp., ISBN 9780080875385, 1986. 
Short summary
Despite its advantages for the simulation of flow in heterogeneous and fractured porous media, the mixed hybrid finite element method has been rarely used for transport as it suffers from strong unphysical oscillations. We develop here a new upwind scheme for the mixed hybrid finite element that can avoid oscillations. Numerical examples confirm the robustness of this new scheme for the simulation of contaminant transport in both saturated and unsaturated conditions.