Abstract.
We prove the convergence of a finite volume scheme for the Richards equation β(p)t-div(λ(β(p)) (νp-ρg) =0, together with a Dirichlet boundary condition and an initial condition, in a bounded domain. We consider the hydraulic charge u=-z as the main unknown function so that no upwinding is necessary. The convergence proof is based on the strong convergence in L2 of the water saturation β(p), which one obtains by estimating differences of space and time translates and applying Kolmogorov’s theorem.
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Received: 30 April 1999 / Revised version: 17 June 1999
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Eymard, R., Gallouët, T., Gutnic, M. et al. Numerical approximation of an elliptic-parabolic equation arising in environment. Comput Visual Sci 3, 33–38 (2000). https://doi.org/10.1007/s007910050049
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DOI: https://doi.org/10.1007/s007910050049