Error estimates for the numerical identification of a variable coefficient

Falk, Richard S.

doi:10.1090/S0025-5718-1983-0689469-3

Error estimates for the numerical identification of a variable coefficient
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by Richard S. Falk PDF

Math. Comp. 40 (1983), 537-546 Request permission

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.

References

Identification and System Parameter Estimation

Philippe G. Ciarlet, The finite element method for elliptic problems, Studies in Mathematics and its Applications, Vol. 4, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1978. MR 0520174
Jim Douglas Jr., Todd Dupont, and Lars Wahlbin, The stability in $L^{q}$ of the $L^{2}$-projection into finite element function spaces, Numer. Math. 23 (1974/75), 193–197. MR 383789, DOI 10.1007/BF01400302

Water Resources Research

P. Lesaint, Finite element methods for symmetric hyperbolic equations, Numer. Math. 21 (1973/74), 244–255. MR 341902, DOI 10.1007/BF01436628
Michael P. Polis and Raymond E. Goodson, Parameter identification in distributed systems: a synthesizing overview, Proc. IEEE 54 (1976), no. 1, 45–61. Recent trends in systems theory. MR 0408888
Gerard R. Richter, Numerical identification of a spatially varying diffusion coefficient, Math. Comp. 36 (1981), no. 154, 375–386. MR 606502, DOI 10.1090/S0025-5718-1981-0606502-3
Ridgway Scott, Interpolated boundary conditions in the finite element method, SIAM J. Numer. Anal. 12 (1975), 404–427. MR 386304, DOI 10.1137/0712032

Soc. Pet. Eng. J.