Robust a-posteriori bounds for non-conforming methods
A talk in the BI.discrete Workshop series by
Matthias Rott from Dortmund
| Abstract: | We present a generalization of the a-posteriori analysis with error dominated oscillation
by Kreuzer and Veeser to non-conforming methods [1].
In contrast to the classical a-posteriori bounds, overestimation cannot occur
because our oscillation term is bounded by the error.
This is of particular interest within the recently developed quasi-optimality framework for non-conforming methods by Veeser and Zanotti [2]. Characteristically, their quasi-optimal a-priori estimates are free of perturbations by classical oscillation, as appearing e.g. in Gudi's medius analysis [3]. The reintroduction of these terms via the a-posteriori analysis would spoil the a-priori achievements and is circumvented by our new approach. We build upon a general a-posteriori framework for the quasi-optimal, non-conforming methods by illustrating our findings for the Crouzeix-Raviart element. This is joint work with Christian Kreuzer, Andreas Veeser and Pietro Zanotti. [1] Christian Kreuzer and Andreas Veeser. Oscillation in a posteriori error estimation. Numer. Math., 148(1):43–78, 2021. [2] Andreas Veeser and Pietro Zanotti. Quasi-optimal nonconforming methods for symmetric elliptic problems. I: Abstract theory. SIAM J. Numer. Anal., 56(3):1621–1642, 2018. [3] Thirupathi Gudi. A new error analysis for discontinuous finite element methods for linear elliptic problems. Math. Comp., 79(272):2169–2189, 2010. Within the CRC this talk is associated to the project(s): A7, B3, B7 |