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Zeitschriftenartikel:

C. Carstensen, M. Feischl, D. Praetorius:
"Rate optimality of adaptive algorithms";
ECCOMAS Newsletter (eingeladen), 07 (2014), S. 20 - 23.



Kurzfassung englisch:
The overwhelming practical success of adaptive mesh-refinement in computational sciences
and engineering has recently obtained a mathematical foundation with a theory on optimal
convergence rates. This article first explains an abstract adaptive algorithm and its marking
strategy. Secondly, it elucidates the concept of optimality in nonlinear approximation theory
for a general audience. It thirdly outlines an abstract framework with fairly general hypotheses
(A1)-(A4) which imply such an optimality result. Various comments conclude this state of the
art overview.

All details and precise references are found in the open access article [Carsten Carstensen,
Michael Feischl, Marcus Page, and Dirk Praetorius: Axioms of adaptivity, Comput. Math. Appl.
67 (2014)] at http://dx.doi.org/10.1016/j.camwa.2013.12.003

http://www.eccomas.org/spacehome/1/22


Elektronische Version der Publikation:
http://publik.tuwien.ac.at/files/PubDat_229929.pdf


Erstellt aus der Publikationsdatenbank der Technischen Universitšt Wien.