Functional a posteriori error estimation for stationary reaction-convection-diffusion problems

Eigel, Martin; Samrowski, Tatiana

doi:10.1515/cmam-2014-0005

Please use this identifier to cite or link to this item: https://doi.org/10.21256/zhaw-29621

Publication type:	Article in scientific journal
Type of review:	Peer review (publication)
Title:	Functional a posteriori error estimation for stationary reaction-convection-diffusion problems
Authors:	Eigel, Martin Samrowski, Tatiana
et. al:	No
DOI:	10.1515/cmam-2014-0005 10.21256/zhaw-29621
Published in:	Computational Methods in Applied Mathematics
Volume(Issue):	14
Issue:	2
Page(s):	135
Pages to:	150
Issue Date:	2014
Publisher / Ed. Institution:	De Gruyter
ISSN:	1609-4840 1609-9389
Language:	English
Subjects:	A posteriori error analysis; Finite element method; Adaptivity; Dominant convection; Functional estimator
Subject (DDC):	510: Mathematics
Abstract:	A functional type a posteriori error estimator for the finite element discretization of the stationary reaction-convection-diffusion equation is derived. In case of dominant convection, the solution for this class of problems typically exhibits boundary layers and shock-front like areas with steep gradients. This renders the accurate numerical solution very demanding and appropriate techniques for the adaptive resolution of regions with large approximation errors are crucial. Functional error estimators as derived here contain no mesh-dependent constants and provide guaranteed error bounds for any conforming approximation. To evaluate the error estimator, a minimization problem is solved which does not require any Galerkin orthogonality or any specific properties of the employed approximation space. Based on a set of numerical examples, we assess the performance of the new estimator. It is observed that it exhibits a good efficiency also with convection-dominated problem settings.
Further description:	Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch)
URI:	https://digitalcollection.zhaw.ch/handle/11475/29621
Fulltext version:	Published version
License (according to publishing contract):	Licence according to publishing contract
Departement:	School of Engineering
Organisational Unit:	Institute of Applied Mathematics and Physics (IAMP)
Appears in collections:	Publikationen School of Engineering

Files in This Item:

File	Description	Size	Format
2014_Eigel-Samrowski_Functional-a-posteriori-error-estimation.pdf		748.44 kB	Adobe PDF	View/Open

Show full item record

Eigel, M., & Samrowski, T. (2014). Functional a posteriori error estimation for stationary reaction-convection-diffusion problems. Computational Methods in Applied Mathematics, 14(2), 135–150. https://doi.org/10.1515/cmam-2014-0005

Eigel, M. and Samrowski, T. (2014) ‘Functional a posteriori error estimation for stationary reaction-convection-diffusion problems’, Computational Methods in Applied Mathematics, 14(2), pp. 135–150. Available at: https://doi.org/10.1515/cmam-2014-0005.

M. Eigel and T. Samrowski, “Functional a posteriori error estimation for stationary reaction-convection-diffusion problems,” Computational Methods in Applied Mathematics, vol. 14, no. 2, pp. 135–150, 2014, doi: 10.1515/cmam-2014-0005.

EIGEL, Martin und Tatiana SAMROWSKI, 2014. Functional a posteriori error estimation for stationary reaction-convection-diffusion problems. Computational Methods in Applied Mathematics. 2014. Bd. 14, Nr. 2, S. 135–150. DOI 10.1515/cmam-2014-0005

Eigel, Martin, and Tatiana Samrowski. 2014. “Functional a Posteriori Error Estimation for Stationary Reaction-Convection-Diffusion Problems.” Computational Methods in Applied Mathematics 14 (2): 135–50. https://doi.org/10.1515/cmam-2014-0005.

Eigel, Martin, and Tatiana Samrowski. “Functional a Posteriori Error Estimation for Stationary Reaction-Convection-Diffusion Problems.” Computational Methods in Applied Mathematics, vol. 14, no. 2, 2014, pp. 135–50, https://doi.org/10.1515/cmam-2014-0005.