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The Galerkin Method for nonlinear parabolic equations of unsteady groundwater flow
Author(s) -
Yoon Yong Sup,
Yeh William WG.
Publication year - 1975
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/wr011i005p00751
Subject(s) - discretization , piecewise , galerkin method , nonlinear system , mathematics , partial differential equation , polynomial , parabolic partial differential equation , mathematical analysis , flow (mathematics) , convergence (economics) , numerical partial differential equations , geometry , physics , quantum mechanics , economics , economic growth
This paper suggests a relatively simple way for solving nonlinear parabolic partial differential equations associated with unsteady groundwater flow. The Galerkin formulation is discretized in the space domain by using piecewise polynomial equations, and the trapezoidal formula is employed to approximate the time derivative. The resulting system of nonlinear equations is then solved by the Newton method. Rapid rate of convergence and easy computer implementation are demonstrated by numerical examples. Results compare favorably with published experimental data.