The boundary element method applied to a moving free boundary problem

In this paper a boundary problem is considered for which the boundary is to be determined as part of the solution. A time-dependent problem involving linear di usion in two spatial dimensions which results in a moving free boundary is posed. The fundamental solution is introduced and Greenʹs Theorem is used to yield a non-linear system of integral equations for the unknown solution and the location of the boundary. The boundary element method is used to obtain a numerical solution to this system of integral equations which in turn is used to obtain the solution of the original problem. Graphical results for a two-dimensional problem are presented.