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A linear backward Euler scheme for the saturation equation: Regularity results and consistency

✍ Scribed by Koffi B. Fadimba

Publisher: Elsevier Science
Year: 2010
Tongue: English
Weight: 664 KB
Volume: 234
Category: Article
ISSN: 0377-0427
DOI: 10.1016/j.cam.2009.12.024

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✦ Synopsis

We consider a linearization of a numerical scheme for the saturation equation (or porous medium equation) ∂S ∂t -∇ • f (S)u -∇ • k(S)∇S = 0, through first order expansions of the fractional function f and the inverse of the function K (s) = s 0 k(τ )dτ , after a regularization of the porous medium equation. We establish a regularity result for the Continuous Galerkin Method and a regularity result for the linearized scheme analogous to the corresponding nonlinear scheme. We then show that the linearized scheme is consistent with the nonlinear scheme analyzed in a previous work.

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