  We propose a parametric finite element method (PFEM) for efficiently solving
the morphological evolution of solid-state dewetting of thin films on a flat
rigid substrate in three dimensions (3D). The interface evolution of the
dewetting problem in 3D is described by a sharp-interface model, which includes
surface diffusion coupled with contact line migration. A variational
formulation of the sharp-interface model is presented, and a PFEM is proposed
for spatial discretization. For temporal discretization, at each time step, we
first update the position of the contact line according to the relaxed contact
angle condition; then, by using the position of the new contact line as the
boundary condition, we solve a linear algebra system resulted from the
discretization of PFEM to obtain the new interface surface for the next step.
The well-posedness of the solution of the PFEM is also established. Extensive
numerical results are reported to demonstrate the accuracy and efficiency of
the proposed PFEM and to show the complexities of the dewetting morphology
evolution observed in solid-state dewetting experiments.
