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Adaptive discontinuous Galerkin methods for nonstationary convection–diffusion problems
journal contribution
posted on 2014-01-23, 09:55 authored by Andrea Cangiani, Emmanuil H. Georgoulis, Stephen MetcalfeThis 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.
History
Citation
IMA Journal of Numerical Analysis 2014, 34 (4), pp. 1578-1597 (20)Alternative title
An a posteriori error estimator for discontinuous Galerkin methods for non-stationary convection-diffusion problemsAuthor affiliation
/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of MathematicsVersion
- AM (Accepted Manuscript)