Error estimate of a fully decoupled numerical scheme based on the Scalar Auxiliary Variable (SAV) method for the Boussinesq system

被引：0

作者：

Zhang, Jun ^{[1
]}

Yuan, Lianghong ^{[2
]}

Chen, Hu ^{[3
]}

机构：

[1] Guizhou Univ Finance & Econ, Computat Math Res Ctr, Guiyang 550025, Peoples R China

[2] Guizhou Univ Finance & Econ, Sch Math & Stat, Guiyang 550025, Peoples R China

[3] Ocean Univ China, Sch Math Sci, Qingdao 266100, Peoples R China

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2024年 / 136卷

基金：

中国国家自然科学基金;

关键词：

SAV; Fully decoupled; Error analysis; Unconditionally stable; Boussinesq equations; PHASE-FIELD MODEL; FINITE-ELEMENT-METHOD; STABLE SCHEMES; 2ND-ORDER; EFFICIENT; APPROXIMATIONS; ALGORITHMS;

D O I：

10.1016/j.cnsns.2024.108102

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we will investigate the unconditional stability and error estimate of the fully decoupled numerical scheme for the Boussinesq equations. The newly constructed numerical scheme is based on the pressure correction technique and the SAV method, in which all coupling terms and nonlinear terms are completely decoupled, that is, we only need to solve several linear constant -coefficient equations. We rigorously prove the unconditional stability and convergence of the time -marching scheme and discuss all the details of the algorithm implementation. Finally, we implement some numerical experiments to verify its stability and accuracy.

引用

页数：14

共 50 条

[21] Linear and fully decoupled scheme for a hydrodynamics coupled phase-field surfactant system based on a multiple auxiliary variables approach
Yang, Junxiang
Tan, Zhijun
Kim, Junseok
JOURNAL OF COMPUTATIONAL PHYSICS, 2022, 452
[22] AN ERROR ESTIMATE FOR A NUMERICAL SCHEME FOR THE COMPRESSIBLE NAVIER-STOKES SYSTEM
Jovanovic, Vladimir
KRAGUJEVAC JOURNAL OF MATHEMATICS, 2007, 30 : 263 - 275
[23] Convergence, error analysis and longtime behavior of the scalar auxiliary variable method for the nonlinear Schrodinger equation
Poulain, Alexandre
Schratz, Katharina
IMA JOURNAL OF NUMERICAL ANALYSIS, 2022, 42 (04) : 2853 - 2883
[24] Optimal error estimates of a second-order fully decoupled finite element method for the nonstationary generalized Boussinesq model
Ding, Qianqian
Hou, Yuanyuan
He, Xiaoming
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2024, 450
[25] A highly efficient and accurate exponential semi-implicit scalar auxiliary variable (ESI-SAV) approach for dissipative system
Liu, Zhengguang
Li, Xiaoli
JOURNAL OF COMPUTATIONAL PHYSICS, 2021, 447
[26] Efficient and Energy Stable Scheme for an Anisotropic Phase-field Dendritic Crystal Growth Model Using the Scalar Auxiliary Variable (SAV) Approach
Yang, Xiaofeng
JOURNAL OF MATHEMATICAL STUDY, 2020, 53 (02): : 212 - 236
[27] A variable time-step IMEX-BDF2 SAV scheme and its sharp error estimate for the Navier-Stokes equations
Di, Yana
Ma, Yuheng
Shen, Jie
Zhang, Jiwei
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS, 2023, 57 (03) : 1143 - 1170
[28] Novel pressure-correction schemes based on scalar auxiliary variable method for the MHD equations
Wang, Weilong
APPLIED MATHEMATICS AND COMPUTATION, 2023, 437
[29] Numerical Researches of Rectangular Barge in Variable Bathymetry Based on Boussinesq-Step Method
Su, Yan
ADVANCES IN CIVIL ENGINEERING, 2022, 2022
[30] Numerical Scheme with Convergence Analysis and Error Estimate for Variable Order Weakly Singular Integro-Differential Equation
Yadav, Poonam
Singh, B. P.
Alikhanov, Anatoly A.
Singh, Vineet Kumar
INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS, 2023, 20 (02)

← 1 2 3 4 5 →