Error estimates for the numerical identification of a variable coefficient
Author:
Richard S. Falk
Journal:
Math. Comp. 40 (1983), 537546
MSC:
Primary 65N99; Secondary 65N30
MathSciNet review:
689469
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Abstract: Error estimates are derived for the approximate identification of an unknown transmissivity coefficient in a partial differential equation describing a model problem in groundwater flow. The approximation scheme considered determines the coefficient by least squares fitting of the observed pressure data.
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 [1]
 G. Chavent, "Identification of distributed parameters," in Identification and System Parameter Estimation, Proc. 3rd IFAC Sympos. (P. Eykhoff, Ed.), pp. 649660.
 [2]
 P. Ciarlet, The Finite Element Method for Elliptic Problems, NorthHolland, Amsterdam, 1978. MR 0520174 (58:25001)
 [3]
 J. Douglas, Jr., T. Dupont & L. Wahlbin, "The stability in of the projection into finite element function spaces," Numer. Math., v. 23, 1975, pp. 193197. MR 0383789 (52:4669)
 [4]
 E. Frind & G. Pinder, "Galerkin solution of the inverse problem for aquifier transmissivity," Water Resources Research, v. 9, 1973, pp. 13971410.
 [5]
 P. Lesaint, "Finite element methods for symmetric hyperbolic equations," Numer. Math., v. 21, 1973, pp. 244255. MR 0341902 (49:6648)
 [6]
 M. P. Polis & R. E. Goodson, "Parameter identification in distributed systems: A synthesizing overview," Proc. IEEE, v. 64, 1976, pp. 4561. MR 0408888 (53:12651)
 [7]
 G. Richter, "Numerical identification of a spatially varying diffusivity coefficient," Math. Comp., v. 36, 1981, pp. 375386. MR 606502 (82c:65055)
 [8]
 R. Scott, "Interpolated boundary conditions in the finite element method," SIAM J. Numer. Anal., v. 12, 1975, pp. 404427. MR 0386304 (52:7162)
 [9]
 Y. S. Yoon & W. W.G. Yeh, "Parameter identification in an inhomogeneous medium with the finiteelement method," Soc. Pet. Eng. J., v. 16, 1976, pp. 217226.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198306894693
PII:
S 00255718(1983)06894693
Keywords:
Inverse problem,
identification problem
Article copyright:
© Copyright 1983
American Mathematical Society
