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

Ying Liu; Xiaoqin Shen; Zhen Guan; Yufeng Nie

doi:10.1016/j.camwa.2023.10.023

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

Ying Liu, Xiaoqin Shen, Zhen Guan, Yufeng Nie

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	449-460
Number of pages	12
Journal	Computers and Mathematics with Applications
Volume	151
DOIs	https://doi.org/10.1016/j.camwa.2023.10.023
State	Published - 1 Dec 2023

Keywords

Adaptive algorithm
Elliptic reconstruction
SAV approach
Weak Galerkin finite element method

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10.1016/j.camwa.2023.10.023

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title = "The adaptive SAV weak Galerkin finite element method for the Allen-Cahn equation",

abstract = "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.",

keywords = "Adaptive algorithm, Elliptic reconstruction, SAV approach, Weak Galerkin finite element method",

author = "Ying Liu and Xiaoqin Shen and Zhen Guan and Yufeng Nie",

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T1 - The adaptive SAV weak Galerkin finite element method for the Allen-Cahn equation

AU - Liu, Ying

AU - Shen, Xiaoqin

AU - Guan, Zhen

AU - Nie, Yufeng

PY - 2023/12/1

Y1 - 2023/12/1

N2 - 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.

AB - 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.

KW - Adaptive algorithm

KW - Elliptic reconstruction

KW - SAV approach

KW - Weak Galerkin finite element method

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DO - 10.1016/j.camwa.2023.10.023

M3 - 文章

AN - SCOPUS:85174701835

SN - 0898-1221

VL - 151

SP - 449

EP - 460

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

ER -

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

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Keywords

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