Institute of Mathematics


Modul:   MAT870  Zurich Colloquium in Applied and Computational Mathematics

Towards optimal adaptivity for time-​dependent problems

Talk by Prof. Dr. Michael Feischl

Date: 16.03.22  Time: 16.30 - 18.00  Room: Y27H35/36

We prove new optimality results for adaptive mesh refinement algorithms for non-​symmetric, indefinite, and time-​dependent problems by proposing a generalization of quasi-​orthogonality which follows directly from the inf-​sup stability of the underlying problem. This completely removes a central technical difficulty in modern proofs of optimal convergence of adaptive mesh refinement algorithms. The main technical tools are new stability bounds for the LU-​factorization of matrices together with a recently established connection between quasi-​orthogonality and matrix factorization.