Zou G.-AWang XSheu T.W.H.TONY W. H. SHEU2021-08-052021-08-0520213784754https://www.scopus.com/inward/record.uri?eid=2-s2.0-85098889921&doi=10.1016%2fj.matcom.2020.12.027&partnerID=40&md5=fbe8c32bfd119b2be5fcc70b59cc4b8bhttps://scholars.lib.ntu.edu.tw/handle/123456789/576860In this paper, we propose a new phase field model involving the p-Laplacian operator with 1<p?2. This newly developed model can be used to simulate the sub-diffuse interface phenomena in the course of phase transitions during microstructure evolution. We also propose an energy-stable finite element approximation for the proposed nonlinear parabolic problem and rigorously prove that the finite element approximation is unconditionally energy stable. Moreover, we give the optimal error estimate and convergence rate with respect to the mesh sizes. Numerical examples are carried out to demonstrate the stability and accuracy of the proposed scheme, which is in accordance with the theoretical ones. Numerical results also indicate that the evolution of free energy is in consistency with the discrete dissipation theory. Moreover, the energy initially decreases sharply when the parameter p becomes larger. Meanwhile, we can observe that the parameter p affects the spatial patterns during phase transition. More precisely, the phase field value will be changed more slowly as well when the parameter p becomes smaller. ? 2021 International Association for Mathematics and Computers in Simulation (IMACS)Finite element method; Free energy; Laplace equation; Laplace transforms; Dissipation theory; Finite element approximations; Micro-structure evolutions; Non-linear parabolic problems; Numerical results; Optimal error estimate; P-Laplacian operator; Phase field models; Mathematical operators[SDGs]SDG7journal article10.1016/j.matcom.2020.12.0272-s2.0-85098889921