| Title:
|
Theoretical and numerical studies of the $P_NP_M$ DG schemes in one space dimension (English) |
| Author:
|
Badenjki, Abdulatif |
| Author:
|
Warnecke, Gerald |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
64 |
| Issue:
|
6 |
| Year:
|
2019 |
| Pages:
|
599-635 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give a proof of the existence of a solution of reconstruction operators used in the $P_NP_M$ DG schemes in one space dimension. Some properties and error estimates of the projection and reconstruction operators are presented. Then, by applying the $P_NP_M$ DG schemes to the linear advection equation, we study their stability obtaining maximal limits of the Courant numbers for several $P_NP_M$ DG schemes mostly experimentally. A numerical study explains how the stencils used in the reconstruction affect the efficiency of the schemes. (English) |
| Keyword:
|
$P_NP_M$ DG scheme |
| Keyword:
|
piecewise polynomial |
| Keyword:
|
projection |
| Keyword:
|
reconstruction |
| Keyword:
|
least square |
| Keyword:
|
local continuous space time Galerkin method |
| Keyword:
|
discontinuous Galerkin |
| Keyword:
|
advection equation |
| Keyword:
|
conservation law |
| Keyword:
|
von Neumann stability analysis |
| Keyword:
|
time discretization |
| MSC:
|
33C45 |
| MSC:
|
65M12 |
| MSC:
|
65M60 |
| idZBL:
|
07144730 |
| idMR:
|
MR4042430 |
| DOI:
|
10.21136/AM.2019.0226-18 |
| . |
| Date available:
|
2019-12-09T11:46:33Z |
| Last updated:
|
2022-01-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147924 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
