Unconditionally energy stable IEQ-FEMs for the Cahn-Hilliard equation and Allen-Cahn equation
<|reference_start|>Unconditionally energy stable IEQ-FEMs for the Cahn-Hilliard equation and Allen-Cahn equation: In this paper, we present several unconditionally energy-stable invariant energy quadratization (IEQ) finite element methods (FEMs) with linear, first- and second-order accuracy for solving both the Cahn-Hilliard equation and the Allen-Cahn equation. For time discretization, we compare three distinct IEQ-FEM schemes that position the intermediate function introduced by the IEQ approach in different function spaces: finite element space, continuous function space, or a combination of these spaces. Rigorous proofs establishing the existence and uniqueness of the numerical solution, along with analyses of energy dissipation for both equations and mass conservation for the Cahn-Hilliard equation, are provided. The proposed schemes' accuracy, efficiency, and solution properties are demonstrated through numerical experiments.<|reference_end|>
@article{chen2024unconditionally,
    title={Unconditionally energy stable IEQ-FEMs for the Cahn-Hilliard equation
  and Allen-Cahn equation},
    author={Yaoyao Chen, Hailiang Liu, Nianyu Yi and Peimeng Yin},
    journal={arXiv preprint arXiv:2402.02712},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.02712},
    primaryClass={math.NA cs.NA}
}