On the identification of soil transmissivity from measurements of the groundwater level
- Bruckner, Gottfried
- Handrock-Meyer, Sybille
- Langmach, Hartmut
2010 Mathematics Subject Classification
- 35R30 86A05 76S05 65N30
- Inverse problems, direct methods, finite elements, linear boundary value problem
This paper is devoted to the inverse problem of identifying a spatially varying coefficient in a linear elliptic differential equation describing the filtration of groundwater. Practice suggests that the gradient of the piezometric head, i.e., Darcy's velocity, may have discontinuities and the transmissivity coefficient is a piecewise constant function.
For solving this problem we have used a direct method of G. Vainikko. Starting at a weak formulation of the problem a suitable discretization is obtained by the method of minimal error. If necessary this method can be combined with Tikhonov's regularization.
The main difficulty consists in generating distributed state observations from measurements of the ground water level. For this step we propose an optimized data preparation procedure using additional information like knowledge of the sought parameter values at some points and lower and upper bounds for the parameter.
First numerical tests show that locally sufficiently many measurements provide locally satisfactory results.