| Title:
|
Unique solvability and stability analysis of a generalized particle method for a Poisson equation in discrete Sobolev norms (English) |
| Author:
|
Imoto, Yusuke |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
64 |
| Issue:
|
1 |
| Year:
|
2019 |
| Pages:
|
33-43 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Unique solvability and stability analysis is conducted for a generalized particle method for a Poisson equation with a source term given in divergence form. The generalized particle method is a numerical method for partial differential equations categorized into meshfree particle methods and generally indicates conventional particle methods such as smoothed particle hydrodynamics and moving particle semi-implicit methods. Unique solvability is derived for the generalized particle method for the Poisson equation by introducing a connectivity condition for particle distributions. Moreover, stability is obtained for the discretized Poisson equation by introducing discrete Sobolev norms and a semi-regularity condition of a family of discrete parameters. (English) |
| Keyword:
|
generalized particle method |
| Keyword:
|
Poisson equation |
| Keyword:
|
unique solvability |
| Keyword:
|
stability |
| Keyword:
|
discrete Sobolev norm |
| MSC:
|
65M12 |
| MSC:
|
65N12 |
| MSC:
|
65N75 |
| idZBL:
|
Zbl 07031675 |
| idMR:
|
MR3913882 |
| DOI:
|
10.21136/AM.2019.0210-18 |
| . |
| Date available:
|
2019-02-08T10:01:31Z |
| Last updated:
|
2021-03-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147593 |
| . |
| 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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| . |
