A posteriori analysis of a Richards problem with a free boundary

Adel Blouza (1) , Linda El Alaoui (2)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem
2 LAGA - Laboratoire Analyse, Géométrie et Applications

Richards equation models the water flow in a partially saturated underground porous medium. When it rains on the surface, boundary conditions of Signorini type may be considered on this part of the boundary. We recall the well-posedness of this problem together with its discretiza-tion by an implicit Euler's scheme in time and finite elements in space. We establish quasi-optimal a posteriori estimates for the solution of the discrete problem. Some numerical experiments confirm the interest of this discretization.

Domaines: Analyse numérique [math.NA]

Adel Blouza, Linda El Alaoui. A posteriori analysis of a Richards problem with a free boundary. 2020. ⟨hal-02444391⟩