Optimal error estimates of a SAV-FEM for the Cahn-Hilliard-Navier-Stokes model

被引：9

作者：

Yang, Jinting ^{[1
]}

Yi, Nianyu ^{[2
]}

Chen, Yaoyao ^{[3
]}

机构：

[1] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China

[2] Xiangtan Univ, Sch Math & Computat Sci, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Hunan, Peoples R China

[3] Anhui Normal Univ, Sch Math & Stat, Wuhu 241000, Anhui, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2024年 / 438卷

关键词：

Cahn-Hilliard-Navier-Stokes equations; Scalar auxiliary variable; Euler semi-implicit scheme; Finite element method; Error estimates; partial differential t; FINITE-ELEMENT APPROXIMATIONS; DIFFUSE-INTERFACE MODEL; PHASE-FIELD MODEL; NONUNIFORM SYSTEM; 2-PHASE FLOWS; FREE-ENERGY; MAC SCHEME; TIME; CONVERGENCE; 2ND-ORDER;

D O I：

10.1016/j.cam.2023.115577

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We carry out the optimal error estimates of a scalar auxiliary variable (SAV) based the Euler semi-implicit finite element method for the Cahn-Hilliard-Navier-Stokes (CHNS) system in this paper. A SAV is introduced to reformulate the CHNS system into an equivalent system. We apply the Euler semi-implicit method and finite element method for the temporal and spatial discretizations to obtain a linear and unconditional energy stable scheme. The stability of numerical solutions under different norms and the optimal error estimates for our proposed numerical schemes are also presented. Finally, numerical examples are presented to demonstrate the accuracy of the proposed method, and the discrete energy is dissipated in numerical simulations. (c) 2023 Elsevier B.V. All rights reserved.

引用

页数：28

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