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 [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.
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© 2016, Society for Industrial and Applied Mathematics.
History
Submitted: 18 May 2015
Accepted: 4 March 2016
Published online: 12 May 2016
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Funding Information
Austrian Science Fund http://dx.doi.org/10.13039/501100002428 : P27005, W1245
Funding Information
Engineering and Physical Sciences Research Council http://dx.doi.org/10.13039/501100000266 : EP/I036427/1
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