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 (Carstensen, Feischl, Page, and Praetorius, Axioms of adaptivity, Comput. Math. Appl., 67 (2014), pp. 1195–1253). We prove that this framework covers standar...

Full description

Bibliographic Details
Main Authors: Feischl, Michael, Praetorius, Dirk, van der Zee, Kristoffer George
Format: Article
Published: Society for Industrial and Applied Mathematics 2016
Subjects:
Online Access:https://eprints.nottingham.ac.uk/32679/
Description
Summary: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.