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.
@article{702736,
title = {Instability of mixed finite elements for Richards' equation},
booktitle = {Programs and Algorithms of Numerical Mathematics},
series = {GDML\_Books},
publisher = {Institute of Mathematics AS CR},
address = {Prague},
year = {2010},
pages = {22-27},
url = {http://dml.mathdoc.fr/item/702736}
}
Březina, Jan. Instability of mixed finite elements for Richards' equation, dans Programs and Algorithms of Numerical Mathematics, GDML_Books, (2010), pp. 22-27. http://gdmltest.u-ga.fr/item/702736/