An abstract analysis of optimal goal-oriented adaptivity

Abstract

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.

References in corpus (4)

• Axioms of Adaptivity
• Analysis-suitable adaptive T-mesh refinement with linear complexity
• Each H^{1/2}-stable projection yields convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data in R^d
• Convergence and Quasi-Optimality of Adaptive FEM with Inhomogeneous Dirichlet Data

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