A Collocation Finite Element Solution for Stefan Problems with Periodic Boundary Conditions

Abstract

     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.