3 Numerical Implementation

The equations (4.50)-(4.52) are solved by means of the finite element method on a sequence of the grids $\Lambda_{h}(t_{0}=0),\Lambda_{h}(t_{1}),\Lambda_{h}(t_{2})$ each one adapted to the position of the void-metal interface from the previous time step. The initial grid $\Lambda _{h}(0)$ is produced by refinement of some basic triangulation $T_h$ of area $T$ according to the initial profile of order parameter $\phi$. The motivation of grid adaptation is to construct and maintain a fine triangulated belt of width $\epsilon\pi$ in the interconnect area where $-1 < \phi < +1$, respectively, where the void-metal interface area is placed.