Strict upper and lower bounds for quantities of interest in static   response sensitivity analysis
  In this paper, a goal-oriented error estimation technique for static response sensitivity analysis is proposed based on the constitutive relation error (CRE) estimation for finite element analysis (FEA). Strict upper and lower bounds of various quantities of interest (QoI) that are associated with the response sensitivity derivative fields are acquired. Numerical results are presented to assess the strict bounding properties of the proposed technique. 
Mengwu Guo and Hongzhi Zhong
math.NA cs.NA