Abstract

This paper presents a symmetric isoparametric finite element formulation for the inverse problem of aquifer transmissivity calculation with known piezometric head. An important aspect of the present formulation is that the groundwater flow equation describing the aquifer behavior is transformed into a second-order differential equation by introducing an artificial variable φ. The two-dimensional, line and transition elements derived based on the weak formulation of this transformed equation possess symmetric matrices. In the formulation of the line elements φ and its derivative in η direction are retained as primary variables. This permits modelling of sudden changes in aquifer width. The transition elements provide a natural connecting link between the two-dimensional elements and the line elements. The line elements provide an efficient means of modelling aquifers with unidirectional flow. Numerical examples are given. A comparison of the results obtained here with the Galerkin finite element solution (nonsymmetric formulation) clearly demonstrates the superiority of the formulation presented here.

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