1985
DOI: 10.1016/0898-1221(85)90156-7
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A numerical procedure for the porous media equation

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Cited by 17 publications
(18 citation statements)
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“…the classical references [23,37,41]. In one space dimension, a key result in the context of deterministic approximations is the one by Russo [48], which applies to the linear diffusion equation, in which the diffusion operator is replaced by a nearest neighbour interaction term (see also later generalizations to nonlinear diffusion in [35]). A recent result which uses the same approach to nonlinear drift diffusion equations is presented in [36].…”
mentioning
confidence: 99%
“…the classical references [23,37,41]. In one space dimension, a key result in the context of deterministic approximations is the one by Russo [48], which applies to the linear diffusion equation, in which the diffusion operator is replaced by a nearest neighbour interaction term (see also later generalizations to nonlinear diffusion in [35]). A recent result which uses the same approach to nonlinear drift diffusion equations is presented in [36].…”
mentioning
confidence: 99%
“…In principle, the proof of Lemma 9 below provides a criterion on the smallness of τ ą 0 that would guarantee the unique solvability of (26). We shall not make this criterion explicit, since in practice, we observe that the Newton method applied to (26) and initialized with x n´1 ∆ always converges to "the right" solution x n ∆ , even for comparatively large steps τ and in rather degenerate situations; we refer the reader to our numerical results in Section 5.…”
Section: Discretization In Timementioning
confidence: 99%
“…Proof. The monotonicity (38) follows (by induction on n) from the definition of x n ∆ as minimizer of F ∆ (·; x n−1 ∆ ):…”
Section: A Priori Estimates and Compactnessmentioning
confidence: 99%