A SCR-based error estimation and adaptive finite element method for the Allen–Cahn equation. (1st July 2019) - Chen, Yaoyao; Huang, Yunqing; Yi, Nianyu
Abstract: In this paper, we consider the adaptive finite element method for the Allen–Cahn equation. The adaptive method is based on a second order accurate unconditionally energy stable finite element scheme and a recovery-type a posteriori error estimator. A SCR-based a posteriori error estimation is derived to control the mesh refinement and coarsening. A time–space adaptive algorithm is proposed for numerical approximation of the Allen–Cahn equation. Numerical experiments are presented to illustrate the reliability and efficiency of the proposed SCR-based error estimator and the corresponding adaptive algorithm. The extension of the proposed adaptive algorithm to the Cahn–Hilliard equation is also discussed.