Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
High Order Whitney Forms on Simplices and the Question of Potentials Read chapter Read first chapter

2021 | OriginalPaper | Chapter

Hierarchical DWR Error Estimates for the Navier-Stokes Equations: h and p Enrichment

Authors : B. Endtmayer, U. Langer, J. P. Thiele, T. Wick

Published in: Numerical Mathematics and Advanced Applications ENUMATH 2019

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this work, we further develop multigoal-oriented a posteriori error estimation for the nonlinear, stationary, incompressible Navier-Stokes equations. It is an extension of our previous work on two-side a posteriori error estimates for the DWR method. We now focus on h enrichment and p enrichment for the error estimator. These advancements are demonstrated with the help of a numerical example.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter On Energy Preserving High-Order Discretizations for Nonlinear Acoustics
next chapter Towards Confident Bayesian Parameter Estimation in Stochastic Chemical Kinetics
Footnotes
Literature
1.
G. Alzetta, D. Arndt, W. Bangerth, V. Boddu, B. Brands, D. Davydov, R. Gassmöller, T. Heister, L. Heltai, K. Kormann, M. Kronbichler, M. Maier, J.-P. Pelteret, B. Turcksin, and D. Wells. The deal.II library, version 9.0. J. Numer. Math., 26(4):173–183, 2018.
2.
R. Becker and R. Rannacher. An optimal control approach to a posteriori error estimation in finite element methods. Acta Numer., 10:1–102, 2001.MathSciNetCrossRef
3.
B. Endtmayer, U. Langer, and T. Wick. Multigoal-oriented error estimates for non-linear problems. J. Numer. Math., 27(4):215–236, 2019.MathSciNetCrossRef
4.
B. Endtmayer, U. Langer, and T. Wick. Two-Side a Posteriori Error Estimates for the Dual-Weighted Residual Method. SIAM J. Sci. Comput., 42(1):A371–A394, 2020.MathSciNetCrossRef
5.
B. Endtmayer and T. Wick. A Partition-of-Unity Dual-Weighted Residual Approach for Multi-Objective Goal Functional Error Estimation Applied to Elliptic Problems. Comput. Methods Appl. Math., 17(4):575–599, 2017.MathSciNetCrossRef
6.
V. Girault and P.-A. Raviart. Finite Element method for the Navier-Stokes equations: theory and algorithms. Number 5 in Computer Series in Computational Mathematics. Springer-Verlag, 1986.
7.
R. Hartmann. Multitarget error estimation and adaptivity in aerodynamic flow simulations. SIAM J. Sci. Comput., 31(1):708–731, 2008.MathSciNetCrossRef
8.
R. Hartmann and P. Houston. Goal-oriented a posteriori error estimation for multiple target functionals. In Hyperbolic problems: theory, numerics, applications, pages 579–588. Springer, Berlin, 2003.
9.
K. Kergrene, S. Prudhomme, L. Chamoin, and M. Laforest. A new goal-oriented formulation of the finite element method. Comput. Methods Appl. Mech. Engrg., 327:256–276, 2017.MathSciNetCrossRef
10.
U. Köcher, M. P. Bruchhäuser, and M. Bause. Efficient and scalable data structures and algorithms for goal-oriented adaptivity of space–time FEM codes. SoftwareX, 10:100239, 2019.CrossRef
11.
D. Pardo. Multigoal-oriented adaptivity for hp-finite element methods. Procedia Computer Science, 1(1):1953–1961, 2010.CrossRef
12.
R. Rannacher and J. Vihharev. Adaptive finite element analysis of nonlinear problems: balancing of discretization and iteration errors. J. Numer. Math., 21(1):23–61, 2013.MathSciNetCrossRef
13.
T. Richter and T. Wick. Variational localizations of the dual weighted residual estimator. J. Comput. Appl. Math., 279:192–208, 2015.MathSciNetCrossRef
14.
M. Schäfer, S. Turek, F. Durst, E. Krause, and R. Rannacher. Benchmark computations of laminar flow around a cylinder. In Flow simulation with high-performance computers II, pages 547–566. Springer, 1996.
15.
E. H. van Brummelen, S. Zhuk, and G. J. van Zwieten. Worst-case multi-objective error estimation and adaptivity. Comput. Methods Appl. Mech. Engrg., 313:723–743, 2017.MathSciNetCrossRef
Metadata
Title
Hierarchical DWR Error Estimates for the Navier-Stokes Equations: h and p Enrichment
Authors
B. Endtmayer
U. Langer
J. P. Thiele
T. Wick
Copyright Year
2021
Book
Numerical Mathematics and Advanced Applications ENUMATH 2019

Print ISBN: 978-3-030-55873-4

Electronic ISBN: 978-3-030-55874-1

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-55874-1_35

Premium Partner

    Image Credits