| Title:
|
Numerical solution of the Kiessl model (English) |
| Author:
|
Dalík, Josef |
| Author:
|
Daněček, Josef |
| Author:
|
Vala, Jiří |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
45 |
| Issue:
|
1 |
| Year:
|
2000 |
| Pages:
|
3-17 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The Kiessl model of moisture and heat transfer in generally nonhomogeneous porous materials is analyzed. A weak formulation of the problem of propagation of the state parameters of this model, which are so-called moisture potential and temperature, is derived. An application of the method of discretization in time leads to a system of boundary-value problems for coupled pairs of nonlinear second order ODE’s. Some existence and regularity results for these problems are proved and an efficient numerical approach based on a certain special linearization scheme and the Petrov-Galerkin method is suggested. (English) |
| Keyword:
|
materials with pore structure |
| Keyword:
|
moisture and heat transport |
| Keyword:
|
nonlinear systems of partial differential equations |
| Keyword:
|
method of discretization in time |
| MSC:
|
65M60 |
| MSC:
|
74F10 |
| MSC:
|
76S05 |
| idZBL:
|
Zbl 1058.65105 |
| idMR:
|
MR1738893 |
| DOI:
|
10.1023/A:1022232632054 |
| . |
| Date available:
|
2009-09-22T18:02:23Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134426 |
| . |
| Reference:
|
[1] J. Appel, P. A. Zabrejko: Nonlinear Superposition Operators.Cambridge tracts inmathematics 95, Cambridge University Press, Cambridge, 1990. MR 1066204 |
| Reference:
|
[2] S. Campanato: Sistemi Ellittici in Forma Divergenza. Regolarita all’interno.Quaderni, Pisa, 1980. Zbl 0453.35026, MR 0668196 |
| Reference:
|
[3] J. Dalík: A Petrov-Galerkin approximation of convection-diffusion and reaction-diffusion problems.Appl. Math. 36 (1991), 329–352. MR 1125636 |
| Reference:
|
[4] J. Dalík, J. Daněček, S. Šťastník: The Kiessl model, existence of the classical solution.Sborník konf. Kočovce (1999), to appear. |
| Reference:
|
[5] J. Dalík, J. Daněček, S. Šťastník: A model of simultaneous distribution of moisture and temperature in porous materials.Ceramics (Silikáty) 41 (2) (1997), 41–46. |
| Reference:
|
[6] J. Dalík, J. Svoboda, S. Šťastník: Návrh matematického modelu šíření vlhkosti a tepla v pórovitém prostředí.Preprint (1997). |
| Reference:
|
[7] D. Gawin, P. Baggio, B. A. Schrefler: Modelling heat and moisture transfer in deformable porous building materials.Arch. Civil Eng. XLII, 3 (1996), 325–349. |
| Reference:
|
[8] M. Giaquinta, G. Modica: Local existence for quasilinear parabolic systems under nonlinear boundary conditions.Ann. Mat. Pura Appl. 149 (1987), 41–59. MR 0932775 |
| Reference:
|
[9] H. Glaser: Graphisches Verfahren zur Untersuchung von Diffusionsvorgängen.Kältetechnik H.10 (1959), 345–349. |
| Reference:
|
[10] J. Kačur: Solution to strongly nonlinear parabolic problems by a linear approximation scheme.Preprint M2-96, Comenius University Bratislava, Faculty of Mathematics and Physics (1996). MR 1670689 |
| Reference:
|
[11] K. Kiessl: Kapillarer und dampfförmiger Feuchtetransport in mehrschichtlichen Bauteilen.Dissertation, Universität in Essen (1983). |
| Reference:
|
[12] J. Nečas: Introduction to the theory of nonlinear elliptic equations.Teubner Texte zur Mathematik 52, Teubner Verlag, Leipzig, 1986. MR 0874752 |
| Reference:
|
[13] J. R. Philip, D. A. de Vries: Moisture movements in porous materials under temperature gradients.Am. Geophys. Union 38 (1957), 222–232. 10.1029/TR038i002p00222 |
| . |
