Domain wall dynamics in magnetic nanodots is critical to the understanding of the magnetization reversal mechanisms in bit-patterned arrays, the issues of writeablility, data rate maximization, and bit stability. In this work, micromagnetic simulations were carried out to investigate the dynamics of domain walls in disk-shaped nanostructures with large built-in perpendicular anisotropy. Due to the strong demagnetizing effect, the domain wall motion falls into the supercritical regime. A 90 degrees phase shift of the wall velocity is developed due to the finite thicknesses. The mean value of the wall velocity increases as the domain wall propagates away from the center. This induced asymmetry causes the frequency of the wall oscillations to be halved. At large diameters, the wall acceleration deceases and the periodicity is lost. The in-plane magnetization configuration shows that multiple spin wave modes are present. The absence of the coherency in the magnetization orientations causes phase canceling. The out-of-phase motion of neighboring segments reduces the wall acceleration.