Goal-Oriented Error Estimation for Cahn-Hilliard Models of Binary Phase Transition

被引：24
作者：
van der Zee, Kristoffer G. [1 ]
Oden, J. Tinsley [1 ]
Prudhomme, Serge [1 ]
Hawkins-Daarud, Andrea [1 ]
机构：
[1] Univ Texas Austin, Inst Computat Engn & Sci, Austin, TX 78712 USA
来源：
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2011年 / 27卷 / 01期
关键词：
a posteriori error estimation; Cahn-Hilliard diffuse interface; dual Cahn-Hilliard; dual well posedness; error residual equivalence; goal oriented error analysis; linearized adjoint; quantities of interest; FINITE-ELEMENT METHODS; FREE-BOUNDARY PROBLEMS; TIME-STEPPING METHODS; PARABOLIC PROBLEMS; EQUATION; ADAPTIVITY; APPROXIMATION;
D O I：
10.1002/num.20638
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A posteriori estimates of errors in quantities of interest are developed for the nonlinear system of evolution equations embodied in the Cahn-Hilliard model of binary phase transition These involve the analysis of wellposedness of dual backward-in-time problems and the calculation of residuals Mixed finite element approximations are developed and used to deliver numerical solutions of representative problems in one- and two dimensional domains Estimated errors are shown to be quite accurate in these numerical examples (C) 2010 Wiley Periodicals Inc Numer Methods Partial Differential Eq 27 160-196 2011
引用
收藏
页码：160 / 196
页数：37
相关论文
共 75 条
  • [1] CONVERGENCE OF THE CAHN-HILLIARD EQUATION TO THE HELE-SHAW MODEL
    ALIKAKOS, ND
    BATES, PW
    CHEN, XF
    [J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1994, 128 (02) : 165 - 205
  • [2] Anderson D.M., 1998, Diffuse-interface methods in fluid mechanics, V30, P139
  • [3] [Anonymous], IMA PREPRINT SERIES
  • [4] [Anonymous], MATH COMP
  • [5] [Anonymous], BLOCKWISE ADAPTIVITY
  • [6] [Anonymous], 2003, Lectures in Mathematics
  • [7] [Anonymous], 1989, Internat. Ser. Numer. Math, DOI DOI 10.1007/978-3-0348-9148-6_3
  • [8] [Anonymous], D
  • [9] [Anonymous], ENCY COMPUTATIONAL M
  • [10] [Anonymous], 2003, Error estimation and adaptive discretization methods in computational fluid dynamics
12345678