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2020 | OriginalPaper | Chapter

Dual Weighted Residual Based Error Control for Nonstationary Convection-Dominated Equations: Potential or Ballast?

Authors : Marius Paul Bruchhäuser, Kristina Schwegler, Markus Bause

Published in: Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2018

Publisher: Springer International Publishing

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Abstract

Even though substantial progress has been made in the numerical approximation of convection-dominated problems, its major challenges remain in the scope of current research by John et al. (Comput Vis Sci 19(5–6):1–17, 2018). In particular, parameter robust a posteriori error estimates for quantities of physical interest and adaptive mesh refinement strategies with proved convergence are still missing. Here, we study numerically the potential of the Dual Weighted Residual (DWR) approach applied to stabilized finite element methods to further enhance the quality of approximations. The impact of a strict application of the DWR methodology is particularly focused rather than the reduction of computational costs for solving the dual problem by interpolation or localization.

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next chapter Automatic Variationally Stable Analysis for FE Computations: An Introduction
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Metadata
Title
Dual Weighted Residual Based Error Control for Nonstationary Convection-Dominated Equations: Potential or Ballast?
Authors
Marius Paul Bruchhäuser
Kristina Schwegler
Markus Bause
Copyright Year
2020
Book
Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2018

Print ISBN: 978-3-030-41799-4

Electronic ISBN: 978-3-030-41800-7

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-41800-7_1

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