Error estimates for the numerical identification of a variable coefficient

Error estimates are derived for the approximate identification of an unknown transmissivity coefficient in a partial differential equation describing a model problem in groundwater now. The approximation scheme considered determines the coefficient by least squares fitting of the observed pressure data. 1. Introduction. In this paper we wish to present an error analysis of a common numerical scheme used in the identification of parameters in distributed systems. Specifically, we shall concern ourselves here with a model problem in groundwater flow. The problem is to identify a spatially varying transmissivity coefficient a(x) from observations of the piezometric head u(x) in a two-dimensional static aquifer s, where a and u are related by the equations (1) -div(avw) =/ inS2,