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Article

Březina, Jan
Instability of mixed finite elements for Richards' equation. (English). In: Chleboun, J., Přikryl, P., Segeth, K. and Šístek, J. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Dolní Maxov, June 6-11, 2010. Institute of Mathematics AS CR, Prague, 2010. pp. 22-27
MSC: 35B50, 76M10, 76S05
Keywords:
Richard's equation; flow in porous media; mixed finite element method; discrete maximum principle
Summary:
Richards' equation is a widely used model of partially saturated flow in a porous medium. In order to obtain conservative velocity field several authors proposed to use mixed or mixed-hybrid schemes to solve the equation. In this paper, we shall analyze the mixed scheme on 1D domain and we show that it violates the discrete maximum principle which leads to catastrophic oscillations in the solution.
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