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A simplified Newton Iteration Method with linear finite elements for transient unsaturated flow
Author(s) -
Li C. W.
Publication year - 1993
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/92wr02891
Subject(s) - discretization , galerkin method , mathematics , finite element method , newton's method , backward euler method , richards equation , flow (mathematics) , nonlinear system , mathematical analysis , basis function , geometry , physics , thermodynamics , soil water , soil science , quantum mechanics , environmental science
A simplified Newton iteration method with Galerkin linear finite elements is developed for the solution of the nonlinear transient unsaturated flow equation in “mixed” form. The use of the Galerkin linear finite element method in the spatial discretization produces a recurrence equation in which the interaode hydraulic conductivity is represented by an integrated average expression which generates the exact Darcy flow flux through each element under the steady horizontal flow condition. The numerical computation of the integrated average hydraulic conductivity using Simpson's 1/3 rule leads to an accurate solution even in the presence of a sharp front. In the time discretization using a backward Euler scheme, the standard Newton iteration method is simplified by taking account of the integrated average expression of the hydraulic conductivity and the diffusion‐dominated nature of the flow process. The resulting two‐level scheme is of the same efficiency on a per‐iteration basis as the modified Picard scheme but converges at a faster rate.