ERROR ESTIMATES FOR SECOND-ORDER SAV FINITE ELEMENT METHOD TO PHASE FIELD CRYSTAL MODEL

被引：7

作者：

Wang, Liupeng ^{[1
]}

Huang, Yunqing ^{[2
]}

机构：

[1] Hunan Inst Engn, Sch Computat Sci & Elect, Xiangtan 411104, Hunan, Peoples R China

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

来源：

ELECTRONIC RESEARCH ARCHIVE | 2021年 / 29卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Error estimates; energy stability; finite element method; scalar auxiliary variable approach; Crank-Nicolson scheme; phase field crystal model; DISCONTINUOUS GALERKIN METHOD; DIFFERENCE SCHEME; CONVERGENCE; STABILITY;

D O I：

10.3934/era.2020089

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, the second-order scalar auxiliary variable approach in time and linear finite element method in space are employed for solving the Cahn-Hilliard type equation of the phase field crystal model. The energy stability of the fully discrete scheme and the boundedness of numerical solution are studied. The rigorous error estimates of order O (tau(2) + h(2)) in the sense of L-2-norm is derived. Finally, some numerical results are given to demonstrate the theoretical analysis.

引用

页码：1735 / 1752

页数：18

共 31 条

[1] Deriving phase field crystal theory from dynamical density functional theory: Consequences of the approximations
Archer, Andrew J.
Ratliff, Daniel J.
Rucklidge, Alastair M.
Subramanian, Priya
[J]. PHYSICAL REVIEW E, 2019, 100 (02)
[2] CONVERGENCE ANALYSIS OF A SECOND ORDER CONVEX SPLITTING SCHEME FOR THE MODIFIED PHASE FIELD CRYSTAL EQUATION
Baskaran, A.
Lowengrub, J. S.
Wang, C.
Wise, S. M.
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2013, 51 (05) : 2851 - 2873
[3] C0 Interior Penalty Methods
Brenner, Susanne C.
[J]. FRONTIERS IN NUMERICAL ANALYSIS - DURHAM 2010, 2012, 85 : 78 - 146
[4] An efficient algorithm for solving the phase field crystal model
Cheng, Mowei
Warren, James A.
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2008, 227 (12) : 6241 - 6248
[5] Phase-field crystal modeling and classical density functional theory of freezing
Elder, K. R.
Provatas, Nikolas
Berry, Joel
Stefanovic, Peter
Grant, Martin
[J]. PHYSICAL REVIEW B, 2007, 75 (06)
[6] Elder KR, 2004, PHYS REV E, V70, DOI 10.1103/PhysRevE.70.051605
[7] Modeling elasticity in crystal growth
Elder, KR
Katakowski, M
Haataja, M
Grant, M
[J]. PHYSICAL REVIEW LETTERS, 2002, 88 (24) : 2457011 - 2457014
[8] Eyre D.J., 1998, An unconditionally stable one-step scheme for gradient systems, P1
[9] An unconditionally energy-stable method for the phase field crystal equation
Gomez, Hector
Nogueira, Xesus
[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2012, 249 : 52 - 61
[10] ENERGY STABLE AND CONVERGENT FINITE ELEMENT SCHEMES FOR THE MODIFIED PHASE FIELD CRYSTAL EQUATION
Grasselli, Maurizio
Pierre, Morgan
[J]. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2016, 50 (05): : 1523 - 1560

← 1 2 3 4 →