Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 54, Issue 3, Pages 1423-1448Publisher
SIAM PUBLICATIONS
DOI: 10.1137/15M1021982
Keywords
adaptivity; goal-oriented algorithm; quantity of interest; convergence; optimal convergence rates; finite element method; boundary element method
Categories
Funding
- Austrian Science Fund (FWF) [P27005]
- FWF doctoral school Dissipation and Dispersion in Nonlinear PDEs [W1245]
- Austrian Science Fund (FWF) [P 27005] Funding Source: researchfish
- Engineering and Physical Sciences Research Council [EP/I036427/1] Funding Source: researchfish
- EPSRC [EP/I036427/1] Funding Source: UKRI
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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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