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|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|
Georgoulis, Emmanuil H.
|Publisher:||Oxford University Press on behalf of the Institute of Mathematics and its Applications|
|Citation:||IMA Journal of Numerical Analysis 2014, 34 (4), pp. 1578-1597 (20)|
|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.|
|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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|CangianiGeorgoulisMetcalfe4.pdf||Post-review (final submitted)||332.96 kB||Unknown||View/Open|
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