Townley, L.R. (1984), Second order effects of uncertain transmissivities on predictions of piezometric heads, Finite Elements in Water Resources, Proceedings of the 5th International Conference, Burlington, Vermont, USA, Springer-Verlag, June 1984.

Finite element techniques are frequently used for deterministic analysis of steady state two-dimensional aquifer flow. When the spatial distribution of transmissivities is uncertain, however, the usual solution for piezometric heads is only correct to first order. Using a Taylor series expansion, it is shown that the mean distribution of heads consists of the usual solution plus a second order correction. Numerical results are presented which show agreement between Monte Carlo solutions and the second order Taylor series solutions for expected heads. An efficient procedure is described which avoids the explicit evaluation of the extremely large second derivative matrix.