We provide an abstract framework for optimal goal-oriented adaptivity for finite element methods and boundary element methods in the spirit of [Carstensen et al., Comput. Math. Appl. 67 (2014)]. We prove that this framework covers standard discretizations of general second-order linear elliptic PDEs and hence generalizes available results [Mommer & Stevenson, SIAM J. Numer. Anal. 47 (2009); Becker et al., SIAM J. Numer. Anal. 49 (2011)] beyond the Poisson equation.
@article{arxiv.1505.04536,
title = {An abstract analysis of optimal goal-oriented adaptivity},
author = {Michael Feischl and Dirk Praetorius and Kristoffer G. van der Zee},
journal= {arXiv preprint arXiv:1505.04536},
year = {2016}
}