Wednesday, August 24, 2022 - 09:45 in V2-210/216
Optimal adaptive algorithms for indefinite and time-dependent problems
A talk in the BI.discrete Workshop series by
Michael Feischl from Vienna
| Abstract: |
In the recent work [Feischl, Math. Comp., 2022], 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 and leads to simple optimality proofs for the Taylor-Hood discretization of the Stokes problem, a finite-element/boundary-element discretization of an unbounded transmission problem, and an adaptive time-stepping scheme for parabolic equations. 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.
Within the CRC this talk is associated to the project(s): B7 |
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