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Technische Universität Dortmund
Fak. Mathematik, LS X
44221 Dortmund

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Technische Universität Dortmund
Fak. Mathematik, LS X
Vogelpothsweg 87
44227 Dortmund


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Vortrag am 18.01.2018 im Rahmen des Oberseminars Numerische Analysis und Optimierung

Zeit: 14.00 Uhr c.t., Mathematikgebäude Raum: M 511

Vortragender: Dr. Michael Feischl, KIT - Karlsruhe Institute of Technology, IANM, Karlsruhe, Deutschland

Rate optimal adaptivity for the Stokes problem

We develop a framework which allows us to prove the essential general quasi-orthogonality for the stationary Stokes problem. General quasi-orthogonality was first proposed in [Carstensen, Feischl, Page, Praetorius 2014] as a necessary ingredient of optimality proofs and is the major difficulty on the way to prove rate optimal convergence of adaptive algorithms for many strongly non-symmetric or indefinite problems. The proof exploits a new connection between the general quasi-orthogonality and LU-factorization of infinite matrices. We then derive that a standard adaptive algorithm for the stationary Stokes problem in 2D converges with optimal rates.