A-posteriori error estimates for pressure-correction schemes
Please always quote using this URN: urn:nbn:de:bvb:29-opus4-75113
- In this thesis, a-posteriori error estimates for time discretizations of the incompressible time dependent Stokes equations by pressure-correction methods are presented.
Pressure-correction methods are splitting schemes, which decouple the velocity and the
pressure. As a result the Stokes equations reduce to much easier schemes, which can
be solved by cost-efficient algorithm. In a first step, a-posteriori estimates for the instationary Stokes system, discretized by the two-step backward differential formula method
(BDF2), are presented. This allows to compare the a-posteriori estimators of the discretized Stokes system with the estimators of the pressure-correction scheme.
In theIn this thesis, a-posteriori error estimates for time discretizations of the incompressible time dependent Stokes equations by pressure-correction methods are presented.
Pressure-correction methods are splitting schemes, which decouple the velocity and the
pressure. As a result the Stokes equations reduce to much easier schemes, which can
be solved by cost-efficient algorithm. In a first step, a-posteriori estimates for the instationary Stokes system, discretized by the two-step backward differential formula method
(BDF2), are presented. This allows to compare the a-posteriori estimators of the discretized Stokes system with the estimators of the pressure-correction scheme.
In the second part of the thesis rigorous proofs of global upper bounds for the incremen-
tal pressure correction scheme discretized by backward Euler scheme as well as for the
two-step backward differential formula method (BDF2) in rotational form are presented.
Moreover, rate optimality of the estimators are shown for velocity (in case of backward
Euler and BDF2 in rotational form) and pressure (in case of Euler). Computational
experiments confirm the theoretical results.…
Author: | Andreas Brenner |
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Persistent identifiers - URN: | urn:nbn:de:bvb:29-opus4-75113 |
Referee: | Eberhard Bänsch, Charalambos Makridakis |
Document Type: | Doctoral Thesis |
Language: | English |
Year of publication: | 2016 |
Date of online publication (Embargo Date): | 2016/07/09 |
Publishing Institution: | Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) |
Granting institution: | Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Naturwissenschaftliche Fakultät |
Acceptance date of the thesis: | 2016/12/08 |
Release Date: | 2016/09/19 |
Tag: | A-posteriori error analysis; fractional step methods; projection methods; reconstruction; two-step backward differentiation formula |
SWD-Keyword: | A-posteriori-Abschätzung; Navier-Stokes-Gleichung |
Institutes: | Naturwissenschaftliche Fakultät |
Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 518 Numerische Analysis |
MSC-Classification: | 65-XX NUMERICAL ANALYSIS |
open_access (DINI-Set): | open_access |
Licence (German): |