Please use this identifier to cite or link to this item: http://hdl.handle.net/2381/28539
Title: Adaptive discontinuous Galerkin methods for nonstationary convection–diffusion problems
Other Titles: An a posteriori error estimator for discontinuous Galerkin methods for non-stationary convection-diffusion problems
Authors: Cangiani, Andrea
Georgoulis, Emmanuil H.
Metcalfe, Stephen
First Published: 30-Oct-2013
Publisher: Oxford University Press on behalf of the Institute of Mathematics and its Applications
Citation: IMA Journal of Numerical Analysis (2013)
Abstract: This work is concerned with the derivation of a robust a posteriori error estimator for a discontinuous Galerkin (dG) method discretization of a linear nonstationary convection–diffusion initial/boundary value problem and with the implementation of a corresponding adaptive algorithm. More specifically, we derive a posteriori bounds for the error in the L[superscript 2](H[superscript 1]) + L∞(L[superscript 2])-type norm for an interior penalty dG discretization in space and a backward Euler discretization in time. Finally, an adaptive algorithm is proposed utilizing the error estimator. Optimal rate of convergence of the adaptive algorithm is observed in a number of test problems and for various Pèclet numbers.
DOI Link: 10.1093/imanum/drt052
ISSN: 0272-4979
eISSN: 1464-3642
Links: http://imajna.oxfordjournals.org/content/early/2013/10/30/imanum.drt052
http://hdl.handle.net/2381/28539
Version: Post-print
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © 2013, The authors. This is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Numerical Analysis following peer review. The definitive publisher-authenticated version IMA Journal of Numerical Analysis (2013) is available online at: http://imajna.oxfordjournals.org/content/early/2013/10/30/imanum.drt052.
Appears in Collections:Published Articles, Dept. of Mathematics

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