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In this study, we develop a phase-field model to investigate the mesoscale kinetics of anisotropic abnormal grain growth in single-phase polycrystalline doped-a-alumina (Nextel 610) fibers at 1300 C. The model incorporates (i) the change of the facet energy of abnormal grains due to grain boundary (GB) complexion transition, (ii) the inclination-dependent GB stiffness and (iii) the anisotropic GB mobility that is linked to the local stiffness inversely. This constitutive coupling provides a mesoscale representation of GB complexion effects on GB kinetics and the plate-like shape of the abnormal grains observed in experimental microstructures. Two- and three-dimensional simulations match the experimentally observed evolution of elongated, faceted abnormal grains within a matrix of fine equiaxed grains and capture the sensitivity of abnormal-grain shape to the set of GB facets and their symmetries. The model provides a computationally efficient framework for simulating highly anisotropic microstructural evolution in ceramic fibers and establishes a basis for future extensions that incorporate dopant diffusion and segregation effects on GB kinetics.