A SCR-based error estimation and adaptive finite element method for the Allen–Cahn equation. (1st July 2019)

• Record Type: Journal Article
• Authors: Chen, Yaoyao; Huang, Yunqing; Yi, Nianyu
• Is Part Of: Computers & mathematics with applications. Volume 78:issue 1(2019)
• Page Start: 204
• Page End: 223
• Publication Date: 2019-07-01
• Subjects: Allen–Cahn equation -- Superconvergent cluster recovery -- A posteriori error estimation -- Adaptive -- Finite element method; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2019.02.022
• Languages: English
• ISSNs: 0898-1221

Abstract

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.