Numerical solutions of elliptic inverse problems via the equation error method

To estimate a parameter in an elliptic boundary value problem, the method of equation error chooses the value that minimizes the error in the PDE and boundary condition (the solution of the BVP having been replaced by a measurement). The estimated parameter converges to the exact value as the measured data converge to the exact value, provided Tikhonov regularization is used to control the instability inherent in the problem. The error in the estimated solution can be bounded in an appropriate quotient norm; estimates can be derived for both the underlying (infinite-dimensional) problem and a finite-element discretization that can be implemented in a practical algorithm. Numerical experiments demonstrate the efficacy and limitations of the method.

VOLUME YIELDS OF SMALLHOLDER Eucalyptus grandis W. HILL EX MAIDEN STANDS IN EASTERN PARAGUAY

Smallholders in eastern Paraguay plant small stands of Eucalyptus grandis W. Hill ex Maiden intended for sale on the local market. Smallholders have been encouraged to plant E. grandis by local forestry extension agents who offer both forestry education and incentive programs. Smallholders who practice recommended forestry techniques geared towards growing large diameter trees of good form are financially rewarded by the local markets which desire saw log quality trees. The question was posed, are smallholders engaging in recommended silvicultural practices and producing reasonable volume yields? It was hypothesized that smallholders, having received forestry education and having financial incentives from the local market, would engage in silvicultural practices resulting in trees of good form and volume yields that were reasonable for the local climate and soil characteristics. Yield volume results from this study support this hypothesis. Mean volume yield was estimated at 70 cubic meters per hectare at age four and 225 cubic meters per hectare at age eight. These volume yields compare favorably to volume yields from other studies of E. grandis grown in similar climates, with similar stocking levels and site qualities.