A posteriori finite element bounds for sensitivity derivatives of partial-differential-equation outputs

We present a Neumann-subproblem a posteriori finite element procedure for t he efficient and accurate calculation of rigorous, "constant-free" upper an d lower bounds for sensitivity derivatives of functionals of the solutions of partial differential equations. The design motivation for sensitivity de rivative error control is discussed; the a posteriori finite element proced ure is described; the asymptotic bounding properties and computational comp lexity of the method are summarized; and illustrative numerical results are presented. (C) 2000 Elsevier Science B.V. All rights reserved.