A priori error estimates for a mixed finite element discretization of the Richard’s equation. (English) Zbl 1075.76042
Summary: A mixed finite element discretization is applied to Richard’s equation, a nonlinear, possibly degenerate parabolic partial differential equation modeling water flow through porous medium. The equation is considered in its pressure formulation and includes both variably and fully saturated flow regime. Characteristic of such problems is the lack in regularity of the solution. To handle this, we use a time-integrated scheme. We analyze the scheme and present error estimates showing its convergence.
MSC:
76M10 | Finite element methods applied to problems in fluid mechanics |
76S05 | Flows in porous media; filtration; seepage |
65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |