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math.NA2026
Discrete positivity and maximum principles for a finite element discretization of the Richards equation
Abderrahmane Benfanich, Yves Bourgault, Abdelaziz Beljadid
Standard finite element discretizations of the Richards equation may violate the discrete minimum principle, producing unphysical negative saturations. While existing bound-preserv…
math.NA2025★ 2 cited
A finite element method using a bounded auxiliary variable for solving the Richards equation
Abderrahmane Benfanich, Yves Bourgault, Abdelaziz Beljadid
The Richards equation, a nonlinear elliptic parabolic equation, is widely used to model infiltration in porous media. We develop a finite element method for solving the Richards eq…