Balanced-norm error estimate of the local discontinuous Galerkin method on layer-adapted meshes for reaction-diffusion problems.
In: Numerical Algorithms, Jg. 91 (2022-12-01), Heft 4, S. 1597-1626
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Zugriff:
We study the local discontinuous Galerkin (LDG) method on layer-adapted meshes for singularly perturbed problems. For these problems of reaction-diffusion type, the balanced norm is suitable to capture the contribution of boundary layer component of the solution. However, it is rather difficult to derive optimal balanced-norm error estimate of the LDG method in the general case. That is, one can only obtain suboptimal error estimate of the LDG method in the mentioned "artificial" norm by using the traditional technique. In this paper, we propose a novel projection which combines the local Gauss-Radau projection with the local L2 projection in a subtle way. We obtain an improved balanced-error estimate. In particular, this estimate is optimal in the case that the regular component of the solution belongs to the finite element space. Numerical experiments are also given to test the theoretical results. [ABSTRACT FROM AUTHOR]
Titel: |
Balanced-norm error estimate of the local discontinuous Galerkin method on layer-adapted meshes for reaction-diffusion problems.
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Autor/in / Beteiligte Person: | Cheng, Yao ; Yan, Li ; Mei, Yanjie |
Zeitschrift: | Numerical Algorithms, Jg. 91 (2022-12-01), Heft 4, S. 1597-1626 |
Veröffentlichung: | 2022 |
Medientyp: | academicJournal |
ISSN: | 1017-1398 (print) |
DOI: | 10.1007/s11075-022-01316-9 |
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