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A Generic stabilization approach for higher order discontinuous galerkin methods for convection dominated problems
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Dedner, Andreas and Klöfkorn, Robert (2011) A Generic stabilization approach for higher order discontinuous galerkin methods for convection dominated problems. Journal of Scientific Computing, Volume 47 (Number 3). pp. 365-388. doi:10.1007/s10915-010-9448-0 ISSN 0885-7474.
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Official URL: http://dx.doi.org/10.1007/s10915-010-9448-0
Abstract
In this paper we present a stabilized Discontinuous Galerkin (DG) method for hyperbolic and convection dominated problems. The presented scheme can be used in several space dimension and with a wide range of grid types. The stabilization method preserves the locality of the DG method and therefore allows to apply the same parallelization techniques used for the underlying DG method. As an example problem we consider the Euler equations of gas dynamics for an ideal gas. We demonstrate the stability and accuracy of our method through the detailed study of several test cases in two space dimension on both unstructured and cartesian grids. We show that our stabilization approach preserves the advantages of the DG method in regions where stabilization is not necessary. Furthermore, we give an outlook to adaptive and parallel calculations in 3d.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Conservation laws (Mathematics), Galerkin methods, Finite volume method | ||||
| Journal or Publication Title: | Journal of Scientific Computing | ||||
| Publisher: | Springer New York LLC | ||||
| ISSN: | 0885-7474 | ||||
| Official Date: | 2011 | ||||
| Dates: |
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| Volume: | Volume 47 | ||||
| Number: | Number 3 | ||||
| Page Range: | pp. 365-388 | ||||
| DOI: | 10.1007/s10915-010-9448-0 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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