(4.3) |

Finally, the discretized equation for point with neighbor points can be written implicitly as

with is the distance between grid point and , as the interface area between the domains and , and as the volume of the domain . For position-dependent , one can use here some average, e.g. . Equation (4.4) can be generally written as

where runs over all neighboring grid points in the same segment, is the flux between points and , and is the source term (see Fig. 4.2). Grid points on the boundary are defined as having neighbor grid points in other segments. Thus, for boundary elements (4.5) does not represent the complete control function , since all fluxes into the contact or the other segment are missing. For that reason, the information for these boxes has to be completed by taking the boundary conditions into account.