The properties of polycrystalline materials are determined by their microstructure. Due to this fact, the kinetics of grain growth play an important role for polycrystalline materials, such as metals, ceramics and intermetallics. For better understanding of these kinetics, an artificial grain topology, consisting of a quadratic, two six-sided, and one eight-sided grain, is designed. The grain growth process is simulated by means of a "Finite Difference"-routine programmed in FORTRAN using an explicit integration scheme. Parameter studies were carried out, where triple point and grain boundary mobilities were varied. The results of these simulations showed, that not only the topology of the microstructure play an important role, but also mobilities of the microstructural entities. All these simulations showed, that the eight-sided grain always grows at the expense of the quadratic grain, independently of their microstructural mobilities. The two six-sided grains grew or shrank differently, depending on their mobilities. It turned out that higher mobilities in triple junctions and grain boundaries do not always lead to larger grains. Lower mobilities provided that the dissipative process can occur and can be associated to abnormal grain growth. Furthermore, the several simulations were compared with calculations from other models found in literature. The simulated results were also compared with micrographs for verification. A broadening of the grain size distribution at small triple point mobilities can be found in the used model and in the experimental data.