Numerical identification of a spatially varying diffusion coefficient

Author:
Gerard R. Richter

Journal:
Math. Comp. **36** (1981), 375-386

MSC:
Primary 65M05; Secondary 65M10

DOI:
https://doi.org/10.1090/S0025-5718-1981-0606502-3

MathSciNet review:
606502

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We consider the inverse problem of identifying a spatially varying diffusion coefficient on the basis of an observed solution to the forward problem. Under appropriate conditions, this inverse problem can be solved as a first order hyperbolic problem in the unknown coefficient. We provide a modified upwind difference scheme for this hyperbolic problem and prove that its convergence rate is when certain conditions are met.

**[1]**Jacob Bear,*Dynamics of Fluids in Porous Media*, American Elsevier, New York, 1972, pp. 214-215.**[2]**Richard S. Falk,*Error estimates for the numerical identification of a variable coefficient*, Math. Comp.**40**(1983), no. 162, 537–546. MR**689469**, https://doi.org/10.1090/S0025-5718-1983-0689469-3**[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. MR**0473443****[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. MR**628945**, https://doi.org/10.1137/0141016

Retrieve articles in *Mathematics of Computation*
with MSC:
65M05,
65M10

Retrieve articles in all journals with MSC: 65M05, 65M10

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1981-0606502-3

Article copyright:
© Copyright 1981
American Mathematical Society