Numerical solution of the Kiessl model

Josef Dalík; Josef Daněček; Jiří Vala

Applications of Mathematics (2000)

  • Volume: 45, Issue: 1, page 3-17
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Dalík, Josef, Daněček, Josef, and Vala, Jiří. "Numerical solution of the Kiessl model." Applications of Mathematics 45.1 (2000): 3-17. <http://eudml.org/doc/33046>.

@article{Dalík2000,
abstract = {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.},
author = {Dalík, Josef, Daněček, Josef, Vala, Jiří},
journal = {Applications of Mathematics},
keywords = {materials with pore structure; moisture and heat transport; nonlinear systems of partial differential equations; method of discretization in time; materials with pore structure; moisture and heat transport; nonlinear systems of partial differential equations; method of discretization in time},
language = {eng},
number = {1},
pages = {3-17},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Numerical solution of the Kiessl model},
url = {http://eudml.org/doc/33046},
volume = {45},
year = {2000},
}

TY - JOUR
AU - Dalík, Josef
AU - Daněček, Josef
AU - Vala, Jiří
TI - Numerical solution of the Kiessl model
JO - Applications of Mathematics
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 45
IS - 1
SP - 3
EP - 17
AB - 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.
LA - eng
KW - materials with pore structure; moisture and heat transport; nonlinear systems of partial differential equations; method of discretization in time; materials with pore structure; moisture and heat transport; nonlinear systems of partial differential equations; method of discretization in time
UR - http://eudml.org/doc/33046
ER -

References

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  9. Graphisches Verfahren zur Untersuchung von Diffusionsvorgängen, Kältetechnik H.10 (1959), 345–349. (1959) 
  10. Solution to strongly nonlinear parabolic problems by a linear approximation scheme, Preprint M2-96, Comenius University Bratislava, Faculty of Mathematics and Physics (1996). (1996) MR1670689
  11. Kapillarer und dampfförmiger Feuchtetransport in mehrschichtlichen Bauteilen, Dissertation, Universität in Essen (1983). (1983) 
  12. Introduction to the theory of nonlinear elliptic equations, Teubner Texte zur Mathematik 52, Teubner Verlag, Leipzig, 1986. (1986) MR0874752
  13. 10.1029/TR038i002p00222, Am. Geophys. Union 38 (1957), 222–232. (1957) DOI10.1029/TR038i002p00222

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