In many engineering applications, the global energy of the problem may be a quantity of limited relevance. This motivated the design of goal-oriented adaptive finite element methods (see e.g. [1,4-6]). They intend to approximate a particular Quantity of Interest (QoI) using an error estimator based on the solution of the adjoint problem to guide the refinements. In this framework, Darrigrand et al. [3] presented an alternative dual operator for the representations of the error in the QoI. In the context of hp-adap…