A SCR-based error estimation and adaptive finite element method for the Allen–Cahn equation

Yaoyao Chen,Yunqing Huang,Nianyu Yi

doi:10.1016/j.camwa.2019.02.022

Yaoyao Chen, Yunqing Huang + Show 1 more

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https://doi.org/10.1016/j.camwa.2019.02.022

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Journal: Computers & Mathematics with Applications	Publication Date: Mar 2, 2019
Citations: 26	License type: publisher-specific-oa

Affiliation: Xiangtan University

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.

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