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We propose an accurate and energy-stable parametric finite element method forsolving the sharp-interface continuum model of solid-state dewetting inthree-dimensional space. The model describes the motion of the film\slash vaporinterface with contact line migration and is governed by the surface diffusionequation with proper boundary conditions at the contact line. We present a newweak formulation for the problem, in which the interface and its contact lineare evolved simultaneously. By using piecewise linear elements in space andbackward Euler in time, we then discretize the weak formulation to obtain afully discretized parametric finite element approximation. The resultingnumerical method is shown to be well-posed and unconditionally energy-stable.Furthermore, the numerical method is extended for solving the sharp interfacemodel of solid-state dewetting with anisotropic surface energies in theRiemmanian metric form. Numerical results are reported to show the convergenceand efficiency of the proposed numerical method as well as the anisotropiceffects on the morphological evolution of thin films in solid-state dewetting.

An Energy-Stable Parametric Finite Element Method for Simulating Solid-state Dewetting Problems in Three Dimensions