An abstract analysis of optimal goal-oriented adaptivity - Feischl, Michael; Praetorius, Dirk; van der Zee, Kristoffer George (Society for Industrial and Applied Mathematics, 2016)
We provide an abstract framework for optimal goal-oriented adaptivity for finite element methods and boundary element methods in the spirit of (Carstensen, Feischl, Page, and Praetorius, Axioms of adaptivity, 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 beyond the Poisson equation.