Numerical analysis of an unconditionally energy-stable reduced-order finite element method for the Allen-Cahn phase field model

被引：0

作者：

Li, Huanrong ^{[1
,2
]}

Wang, Dongmei ^{[1
]}

Song, Zhengyuan ^{[1
]}

Zhang, Fuchen ^{[1
]}

机构：

[1] Chongqing Technol & Business Univ, Coll Math & Stat, Chongqing 400067, Peoples R China

[2] Chongqing Technol & Business Univ, Chongqing Key Lab Social Econ & Appl Stat, Chongqing 400067, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2021年 / 96卷

基金：

美国国家科学基金会;

关键词：

Allen-Cahn model; POD technique; SFE; SROFE; Error estimates; PROPER ORTHOGONAL DECOMPOSITION; DISCONTINUOUS GALERKIN METHOD; HILLIARD; EQUATION; H-2-REGULARITY; APPROXIMATION; SCHEMES; UNIFORM;

D O I：

10.1016/j.camwa.2021.05.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a reduced-order finite element (FE) method preserving the unconditional energy-stability is proposed to simulate the Allen-Cahn phase field model, based on the proper orthogonal decomposition (POD) method with the snapshot technique. We first derive the full order FE formulation of the Allen-Cahn model and compute its FE full solutions, from which we choose a few spatio-temporal solutions as snapshots. Based on the POD technique, we then build a set of optimal POD bases maximizing the energy content in the original ensemble data, and in the new low-dimensional space spanned by the POD bases, we establish a low-order numerical model of stable reduced-order FE (SROFE) formulation for the Allen-Cahn phase field model. We also prove error estimates of the SROFE solutions of the Allen-Cahn phase field model. Finally, some numerical results are provided to test the validity of the SROFE formulation.

引用

页码：67 / 76

页数：10

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