AN ABSTRACT ANALYSIS OF OPTIMAL GOAL-ORIENTED ADAPTIVITY

作者：Feischl Michael; Praetorius Dirk; Van der Zee Kristoffer G

来源：SIAM Journal on Numerical Analysis, 2016, 54(3): 1423-1448.

DOI：10.1137/15M1021982

• adaptivity
• goal-oriented algorithm
• quantity of interest
• convergence
• optimal convergence rates
• finite element method
• boundary element method

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.

• 出版日期2016