| Title:
|
A study of Galerkin method for the heat convection equations (English) |
| Author:
|
Vinogradova, Polina |
| Author:
|
Zarubin, Anatoli |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
57 |
| Issue:
|
1 |
| Year:
|
2012 |
| Pages:
|
71-91 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper investigates the Galerkin method for an initial boundary value problem for heat convection equations. New error estimates for the approximate solutions and their derivatives in strong norm are obtained. (English) |
| Keyword:
|
approximate solution |
| Keyword:
|
error estimate |
| Keyword:
|
Galerkin method |
| Keyword:
|
heat convection equation |
| Keyword:
|
orthogonal projection |
| Keyword:
|
viscous fluid |
| MSC:
|
35K90 |
| MSC:
|
35Q35 |
| MSC:
|
65J10 |
| MSC:
|
65M15 |
| MSC:
|
65M60 |
| idZBL:
|
Zbl 1249.65119 |
| idMR:
|
MR2891306 |
| DOI:
|
10.1007/s10492-012-0005-z |
| . |
| Date available:
|
2012-01-09T19:26:30Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141819 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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[4] Beckenbach, E., Bellman, R.: Inequalities.Springer Berlin (1965). Zbl 0186.09605, MR 0192009 |
| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
[8] Glushko, V. P., Krejn, S. G.: Inequalities for the norms of derivative in spaces $L_p$ with weight.Sibirsk. Mat. Zh. 1 (1960), 343-382 Russian. MR 0133681 |
| Reference:
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[9] Krejn, S. G.: Linear Differential Equations in Banach Spaces. Trans. Math. Monographs, Vol. 29.AMS Providence (1972). |
| Reference:
|
[10] Ladyzhenskaya, O. A.: The Mathematical Theory of Viscous Incompressible Flow.Gordon and Breach New York (1969). Zbl 0184.52603, MR 0254401 |
| Reference:
|
[11] Ladyzhenskaya, O. A., Solonnikov, V. A., Ural'tseva, N. N.: Linear and Quasilinear Equations of Parabolic Type.Nauka Moscow (1967), English transl.: Trans. Math. Monographs, Vol. 23 AMS Rhode Island (1968). Zbl 0164.12302 |
| Reference:
|
[12] Shinbrot, M., Kotorynski, W. P.: The initial value problem for a viscous heat-conducting equations.J. Math. Anal. Appl. 45 (1974), 1-22. MR 0361474, 10.1016/0022-247X(74)90115-2 |
| Reference:
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[13] Solonnikov, V. A.: On estimates of the solutions of elliptic and parabolic systems in $L_p$.Tr. MIAN SSSR 102 (1967), 137-160 Russian. MR 0228809 |
| Reference:
|
[14] Temam, R.: Navier-Stokes Equations. Theory and Numerical Analysis. Rev. ed.North-Holland Publishing Company Amsterdam (1979). Zbl 0426.35003 |
| Reference:
|
[15] Vinogradova, P., Zarubin, A.: Projection method for Cauchy problem for operator-differential equation.Numer. Funct. Anal. Optim. 30 (2009), 148-167. MR 2492080, 10.1080/01630560902735132 |
| Reference:
|
[16] Werne, J., DeLuca, E. E., Rosner, R., Cattaneo, F.: Numerical simulation of soft and hard turbulence: preliminary results for two-dimensional convection.Phys. Rev. Lett. 64 (1990), 2370-2373. 10.1103/PhysRevLett.64.2370 |
| . |
