Mathematikgebäude, Raum M 511

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.

Dr. Michael Feischl

KIT - Karlsruhe Institute of Technology, IANM, Karlsruhe, Deutschland