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Numerical identification of a spatially varying diffusion coefficient. (English) Zbl 0474.65065


MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35R30 Inverse problems for PDEs
35K05 Heat equation
35L45 Initial value problems for first-order hyperbolic systems
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References:

[1] Jacob Bear, Dynamics of Fluids in Porous Media, American Elsevier, New York, 1972, pp. 214-215. · Zbl 1191.76001
[2] Richard S. Falk, Error estimates for the numerical identification of a variable coefficient, Math. Comp. 40 (1983), no. 162, 537 – 546. · Zbl 0551.65083
[3] E. O. Frind & G. F. Pinder, ”Galerkin solution of the inverse problem for aquifer transmissivity,” Water Resour. Res., v. 9, 1973, pp. 1397-1410.
[4] David Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, Berlin-New York, 1977. Grundlehren der Mathematischen Wissenschaften, Vol. 224. · Zbl 0361.35003
[5] R. W. Nelson, ”In-place determination of permeability distribution for heterogeneous porous media through analysis of energy dissipation,” Soc. Pet. Eng. J., v. 8, 1968, pp. 33-42.
[6] D. A. Nutbrown, ”Identification of parameters in a linear equation of groundwater flow,” Water Resour. Res., v. 11, 1975, pp. 581-588.
[7] Gerard R. Richter, An inverse problem for the steady state diffusion equation, SIAM J. Appl. Math. 41 (1981), no. 2, 210 – 221. · Zbl 0501.35075 · doi:10.1137/0141016
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