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.show moreshow less

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Metadaten
Author:Andreas Brenner
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):Keine Creative Commons Lizenz - es gilt der Veröffentlichungsvertrag und das deutsche Urheberrecht
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