Error estimates for time discretizations of Cahn-Hilliard and Allen-Cahn phase-field models for two-phase incompressible flows

被引：39

作者：

Cai, Yongyong ^{[1
,2
]}

Choi, Heejun ^{[2
]}

Shen, Jie ^{[2
]}

机构：

[1] Beijing Computat Sci Res Ctr, Beijing 100193, Peoples R China

[2] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

来源：

NUMERISCHE MATHEMATIK | 2017年 / 137卷 / 02期

基金：

美国国家科学基金会;

关键词：

FINITE-ELEMENT APPROXIMATIONS; PROJECTION METHODS; FLUIDS; EQUATION; DENSITIES;

D O I：

10.1007/s00211-017-0875-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We carry out rigorous error analysis for some energy stable time discretization schemes developed in Shen and Yang (SIAM J Sci Comput 32(3):1159-1179, 2010) for a Cahn-Hilliard phase-field model and in Shen and Yang (Chin Ann Math Ser B 31(5):743-758, 2010) for an Allen-Cahn phase-field model.

引用

页码：417 / 449

页数：33

共 24 条

[1] Diffuse-interface methods in fluid mechanics [J].

Anderson, DM ;

McFadden, GB ;

Wheeler, AA .

ANNUAL REVIEW OF FLUID MECHANICS, 1998, 30 :139-165

[2]

[Anonymous], 1984, Navier-Stokes equations, theory and numerical analysis

[3] ANALYSIS OF A MIXED FINITE ELEMENT METHOD FOR A CAHN-HILLIARD-DARCY-STOKES SYSTEM [J].

Diegel, Amanda E. ;

Feng, Xiaobing H. ;

Wise, Steven M. .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2015, 53 (01) :127-152

[4] THE GLOBAL DYNAMICS OF DISCRETE SEMILINEAR PARABOLIC EQUATIONS [J].

ELLIOTT, CM ;

STUART, AM .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1993, 30 (06) :1622-1663

[5] Unconditionally gradient stable time marching the Cahn-Hilliard equation [J].

Eyre, DJ .

COMPUTATIONAL AND MATHEMATICAL MODELS OF MICROSTRUCTURAL EVOLUTION, 1998, 529 :39-46

[6] Error analysis of a mixed finite element method for the Cahn-Hilliard equation [J].

Feng, XB ;

Prohl, A .

NUMERISCHE MATHEMATIK, 2004, 99 (01) :47-84

[7] Numerical analysis of the Allen-Cahn equation and approximation for mean curvature flows [J].

Feng, XB ;

Prohl, A .

NUMERISCHE MATHEMATIK, 2003, 94 (01) :33-65

[8] Analysis of finite element approximations of a phase field model for two-phase fluids [J].

Feng, Xiaobing ;

He, Yinnian ;

Liu, Chun .

MATHEMATICS OF COMPUTATION, 2007, 76 (258) :539-571

[9] Fully discrete finite element approximations of the Navier-Stokes-Cahn-Hilliard diffuse interface model for two-phase fluid flows [J].

Feng, Xiaobing .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2006, 44 (03) :1049-1072

[10]

GLOwINSKI R., 2003, Handbook of Numerical Analysis, V9, P3, DOI DOI 10.1016/S1570-8659(03)09003-3

← 1 2 3 →