AN INVERSE PROBLEM FROM 2D GROUNDWATER MODELING

The paper is devoted to the inverse problem of identifying the coeffic ient in the main term of an elliptic differential equation describing the filtration of ground water. Experience suggests that the gradient of the piezometric head, i.e. Darcy's velocity, may have discontinuiti es and the transmissivity coefficient is a piecewise constant function . To solve this problem we use a modification of a direct method of Va inikko. Starting with a weak formulation of the problem, a suitable di scretization is obtained by the method of least error. If necessary, t his method can be combined with Tikhonov's regularization. The main di fficulty consists of generating distributed state observations from me asurements of the ground-water level. For this step we propose an opti mized data preparation procedure using additional information such as knowledge oi the sought parameter values at some points and lower and upper bounds for the parameter. Numerical tests confirm the expected l ocal behaviour of the method, i.e. locally sufficiently many measureme nts provide locally satisfactory results. Two numerical examples, one with simulated data and the other with real life data, are given.