Open AccessA collocation finite element solution for Stefan problems with periodic boundary conditions
Author(s) -
Hatice Karabenli,
Yusuf Uçar,
Nesligül Aksan
Publication year - 2016
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1603699k
Subject(s) - mathematics , mathematical analysis , boundary knot method , collocation (remote sensing) , finite element method , singular boundary method , boundary (topology) , oscillation (cell signaling) , boundary value problem , collocation method , mixed finite element method , stefan problem , method of fundamental solutions , boundary element method , differential equation , physics , genetics , biology , thermodynamics , geology , ordinary differential equation , remote sensing
In this study, we are going to obtain some numerical solutions of Stefan problems given together with time-dependent periodic boundary conditions. After using variable space grid method, we have presented a numerical finite element scheme based on collocation finite element method formed with cubic B-splines. The newly obtained numerical results are presented for temperature distribution, the position and the velocity of moving boundary. It is shown that size of the domain, oscillation amplitude and oscillation frequency which are situated at the boundary condition, strongly influence the temperature distribution and position of moving boundary. The numerical results are compared with other numerical solutions obtained by using finite difference method and they are found to be in good agreement with each other.
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