Towards optimal adaptivity for time-​dependent problems

Vortrag von Prof. Dr. Michael Feischl

Datum: 16.03.22  Zeit: 16.30 - 18.00  Raum: 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.