The adaptive SAV weak Galerkin finite element method for the Allen-Cahn equation

Ying Liu, Xiaoqin Shen, Zhen Guan, Yufeng Nie

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1 引用 (Scopus)

摘要

In this paper, the weak Galerkin finite element method with the scalar auxiliary variable (SAV) approach is considered for the Allen-Cahn equation. Based on the elliptic reconstruction technique, the elliptic equation corresponding to the Allen-Cahn equation is introduced, which is employed to split the numerical error into the elliptic error and the parabolic error. Then the weak gradient recovery type a posteriori error estimator of the elliptic equation is adopted to develop the time-space adaptive algorithm. The effectiveness of the SAV weak Galerkin finite element method and the time-space adaptive algorithm is verified by several numerical benchmarks on both uniform and adaptive meshes.

源语言英语
页(从-至)449-460
页数12
期刊Computers and Mathematics with Applications
151
DOI
出版状态已出版 - 1 12月 2023

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