- Tytuł:
- Approximation of a Solidification Problem
- Autorzy:
-
Aboulaich, R.
Haggouch, I.
Souissi, A. - Powiązania:
- https://bibliotekanauki.pl/articles/908072.pdf
- Data publikacji:
- 2001
- Wydawca:
- Uniwersytet Zielonogórski. Oficyna Wydawnicza
- Tematy:
-
optymalizacja
metoda elementów skończonych
Stefan problem
free boundary
shape optimization
Euler method
finite element method - Opis:
- A two-dimensional Stefan problem is usually introduced as a model of solidification, melting or sublimation phenomena. The two-phase Stefan problem has been studied as a direct problem, where the free boundary separating the two regions is eliminated using a variational inequality (Baiocci, 1977; Baiocchi et al., 1973; Rodrigues, 1980; Saguez, 1980; Srunk and Friedman, 1994), the enthalpy function (Ciavaldini, 1972; Lions, 1969; Nochetto et al.., 1991; Saguez, 1980), or a control problem (El Bagdouri, 1987; Peneau, 1995; Saguez, 1980). In the present work, we provide a new formulation leading to a shape optimization problem. For a semidiscretization in time, we consider an Euler scheme. Under some restrictions related to stability conditions, we prove an L^2-rate of convergence of order 1 for the temperature. In the last part, we study the existence of an optimal shape, compute the shape gradient, and suggest a numerical algorithm to approximate the free boundary. The numerical results obtained show that this method is more efficient compared with the others.
- Źródło:
-
International Journal of Applied Mathematics and Computer Science; 2001, 11, 4; 921-955
1641-876X
2083-8492 - Pojawia się w:
- International Journal of Applied Mathematics and Computer Science
- Dostawca treści:
- Biblioteka Nauki
Artykuł