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Galerkin solution of the inverse problem for aquifer transmissivity
Author(s) -
Frind Emil O.,
Pinder George F.
Publication year - 1973
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/wr009i005p01397
Subject(s) - aquifer , finite element method , galerkin method , hydraulic head , mathematics , uniqueness , streamlines, streaklines, and pathlines , inverse problem , mathematical analysis , head (geology) , isotropy , geometry , mechanics , geology , geotechnical engineering , groundwater , physics , quantum mechanics , geomorphology , thermodynamics
The inverse problem in aquifer analysis may be solved by a Galerkin finite element approach. The proposed solution is applied to an inhomogeneous isotropic aquifer for which steady state piezometric head is known and transmissivity is unknown. The condition for existence and uniqueness of a solution is that transmissivity must be known along a line crossed by all streamlines in the flow system. In the Galerkin solution this condition may be stated alternatively in terms of flux, so that knowing the discharge at a well may satisfy the uniqueness requirement. Isoparametric finite elements are used, polynomial shape functions approximating aquifer geometry, hydraulic head, and transmissivity. The flexibility of the isoparametric elements permits using an irregular grid with nodes directly at observation points. Applications show that the solution is highly sensitive to the degree of approximation in the functional representation of hydraulic head but relatively insensitive to the representation of transmissivity. The finite element solution converges to a unique solution as element size decreases.