In this study, the models based on the finite elements approach rather than the geometric transformation methods that are insufficient especially in the applications on larger areas and continuity problem are investigated. In the first step of the study, the project area is divided into solution regions and piecewise defined trial functions are determined for each region. These functions are continuous throughout the project area and yield much better solutions than defining the whole area with a single function. Continuity are defined between the solution regions and the continuities,$C_0$, $C_1$ and $C_2$, are evaluated in the model and reflected in the solution. Furthermore, the continuity can also be provided for the studies performed in the neighboring areas. In the second phase, the common points in the solution regions are transformed into triangular elements by triangulation. Triangular elements are formed up with respect to the principles of continuity, and a separate triangular coordinate system is defined for each triangle. A function to be used for an inner-triangle interpolation in the triangular coordinate system is obtained by using the values of functions and derivations of trial function on the edge points of the triangles. By this function, the transformation value of a point is calculated without any residuals for the common points.