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 2 (H 1) + L 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.
Adaptive discontinuous Galerkin methods for nonstationary convection-diffusion problems / Cangiani, A.; Georgoulis, E. H.; Metcalfe, S.. - In: IMA JOURNAL OF NUMERICAL ANALYSIS. - ISSN 1464-3642. - 34:4(2014), pp. 1578-1597. [10.1093/imanum/drt052]
Adaptive discontinuous Galerkin methods for nonstationary convection-diffusion problems
Cangiani A.
;
2014-01-01
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 2 (H 1) + L 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.File | Dimensione | Formato | |
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