| Title:
|
Some abstract error estimates of a finite volume scheme for a nonstationary heat equation on general nonconforming multidimensional spatial meshes (English) |
| Author:
|
Bradji, Abdallah |
| Author:
|
Fuhrmann, Jürgen |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
58 |
| Issue:
|
1 |
| Year:
|
2013 |
| Pages:
|
1-38 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A general class of nonconforming meshes has been recently studied for stationary anisotropic heterogeneous diffusion problems, see Eymard et al. (IMA J. Numer. Anal. 30 (2010), 1009–1043). Thanks to the basic ideas developed in the stated reference for stationary problems, we derive a new discretization scheme in order to approximate the nonstationary heat problem. The unknowns of this scheme are the values at the centre of the control volumes, at some internal interfaces, and at the mesh points of the time discretization. We derive error estimates in discrete norms $\Bbb L^{\infty }(0,T;H^1_0(\Omega ))$ and ${\Cal W}^{1,\infty }(0,T;L^2(\Omega ))$, and an error estimate for an approximation of the gradient, in a general framework in which the discrete bilinear form involved in the finite volume scheme satisfies some ellipticity condition. (English) |
| Keyword:
|
non-conforming grid |
| Keyword:
|
nonstationary heat equation |
| Keyword:
|
several space dimension |
| Keyword:
|
SUSHI scheme |
| Keyword:
|
implicit scheme |
| Keyword:
|
discrete gradient |
| MSC:
|
35K15 |
| MSC:
|
65M08 |
| MSC:
|
65M15 |
| MSC:
|
65M50 |
| idZBL:
|
Zbl 1274.65251 |
| idMR:
|
MR3022767 |
| DOI:
|
10.1007/s10492-013-0001-y |
| . |
| Date available:
|
2013-01-23T10:09:44Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143131 |
| . |
| Reference:
|
[1] Bradji, A., Fuhrmann, J.: Error estimates of the discretization of linear parabolic equations on general nonconforming spatial grids.C. R. Math. Acad. Sci. Paris 348 (2010), 1119-1122. Zbl 1201.65167, MR 2735020, 10.1016/j.crma.2010.09.020 |
| Reference:
|
[2] Bradji, A., Fuhrmann, J.: Some error estimates for the discretization of parabolic equations on general multidimensional nonconforming spatial meshes.NMA 2010, LNCS 6046 (2011) 269-276 I. Domov, S. Dimova, N. Kolkovska Springer Berlin (2011). MR 2794714 |
| 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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