An Abstract Analysis of Optimal Goal-Oriented Adaptivity

We provide an abstract framework for optimal goal-oriented adaptivity for finite element methods and boundary element methods in the spirit of [C. Carstensen et al., Comput. Math. Appl., 67 (2014), pp. 1195--1253]. We prove that this framework covers standard discretizations of general second-order linear elliptic PDEs and hence generalizes available results [R. Becker, E. Estecahandy, and D. Trujillo, SIAM J. Numer. Anal., 49 (2011), pp. 2451--2469, M. S. Mommer and R. Stevenson, SIAM J. Numer. Anal., 47 (2009), pp. 861--886] beyond the Poisson equation.