Existence of weak solutions is established for the Richards equation in weighted Sobolev spaces via semi-implicit discretization and monotone operators, with the auxiliary variable preserving saturation bounds and the L-scheme showing unconditional linear convergence.
Moussa, Some variants of the classical Aubin–Lions Lemma, Journal of Evolution Equations 16 (1) (2016) 65–93
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Mathematical analysis for a doubly degenerate parabolic equation: Application to the Richards equation
Existence of weak solutions is established for the Richards equation in weighted Sobolev spaces via semi-implicit discretization and monotone operators, with the auxiliary variable preserving saturation bounds and the L-scheme showing unconditional linear convergence.