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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:234

Article

Fadimba, Koffi B.

关键词: Regularity estimates;    Linearization;    Porous medium;    Nonlinear scheme;    Degenerate equation;    Saturation equation;    Backward Euler scheme;   

DOI  :  10.1016/j.cam.2009.12.024

来源: Elsevier

【 摘 要 】

We consider a linearization of a numerical scheme for the saturation equation (or porous medium equation) partial derivative s/partial derivative t - del.f (S)u - del.k(S)del S = 0. through first order expansions of the fractional function f and the inverse of the function K(s) = integral(s)(0) k(tau)d tau, 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. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free