메뉴 건너뛰기




Volumn 37, Issue 1, 2000, Pages 246-268

A discontinuous finite element method for solving a multiwell problem

Author keywords

Finite element method; Materials science; Microstructure; Multiscale; Multiwell problem; Nonconvex minimization; Nonlinear conjugate gradients; Nonlinear elasticity; Shape memory alloys

Indexed keywords


EID: 0003257384     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/s0036142998333791     Document Type: Article
Times cited : (9)

References (24)
  • 1
    • 33750297145 scopus 로고
    • Fine phase mixtures as minimizers of energy
    • J. BALL AND R. JAMES, Fine phase mixtures as minimizers of energy, Arch. Rational. Mech. Anal., 100 (1987), pp. 13-52.
    • (1987) Arch. Rational. Mech. Anal. , vol.100 , pp. 13-52
    • Ball, J.1    James, R.2
  • 2
    • 0002854369 scopus 로고
    • Proposed experimental tests of a theory of fine microstructure and the two-well problem
    • J. BALL AND R. JAMES, Proposed experimental tests of a theory of fine microstructure and the two-well problem, Philos. Trans. Roy. Soc. London Ser. A, 338 (1992), pp. 389-450.
    • (1992) Philos. Trans. Roy. Soc. London Ser. a , vol.338 , pp. 389-450
    • Ball, J.1    James, R.2
  • 4
    • 0031533725 scopus 로고    scopus 로고
    • Numerical solution of the scalar double-well problem allowing microstructure
    • C. CARSTENSEN AND P. PLECHÁČ, Numerical solution of the scalar double-well problem allowing microstructure, Math. Comp., 66 (1997), pp. 997-1026.
    • (1997) Math. Comp. , vol.66 , pp. 997-1026
    • Carstensen, C.1    Plecháč, P.2
  • 5
    • 0026907665 scopus 로고
    • Numerical approximations in variational problems with potential wells
    • M. CHIPOT AND C. COLLINS, Numerical approximations in variational problems with potential wells, SIAM J. Numer. Anal., 29 (1992), pp. 1002-1019.
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 1002-1019
    • Chipot, M.1    Collins, C.2
  • 10
    • 0041740075 scopus 로고
    • Comparison of computational results for twinning in the two-well problem
    • C. Rogers and G. Wallace, eds., Technomic
    • C. COLLINS, Comparison of computational results for twinning in the two-well problem, in Proceedings of the 2nd International Conference on Intelligent Materials, C. Rogers and G. Wallace, eds., Technomic, 1994, pp. 391-401.
    • (1994) Proceedings of the 2nd International Conference on Intelligent Materials , pp. 391-401
    • Collins, C.1
  • 11
    • 0038986483 scopus 로고    scopus 로고
    • Convergence of a reduced integration method for computing microstructures
    • C. COLLINS, Convergence of a reduced integration method for computing microstructures, SIAM J. Numer. Anal., 35 (1998), pp. 1271-1298.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 1271-1298
    • Collins, C.1
  • 14
    • 0028380768 scopus 로고
    • Numerical analysis of a nonconvex variational problem related to solid-solid phase transitions
    • P. GREMAUD, Numerical analysis of a nonconvex variational problem related to solid-solid phase transitions, SIAM J. Numer. Anal., 31 (1994), pp. 111-127.
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 111-127
    • Gremaud, P.1
  • 15
    • 0030353045 scopus 로고    scopus 로고
    • Analysis of a class of nonconforming finite elements for crystalline microstructure
    • P. KLOUČEK, B. LI, AND M. LUSKIN, Analysis of a class of nonconforming finite elements for crystalline microstructure, Math. Comp., 67 (1996), pp. 1111-1125.
    • (1996) Math. Comp. , vol.67 , pp. 1111-1125
    • Klouček, P.1    Li, B.2    Luskin, M.3
  • 16
    • 0000934468 scopus 로고
    • The computation of the dynamics of martensitic microstructure
    • P. KLOUČEK AND M. LUSKIN, The computation of the dynamics of martensitic microstructure, Contin. Mech. Thermodyn., 6 (1994), pp. 209-240.
    • (1994) Contin. Mech. Thermodyn. , vol.6 , pp. 209-240
    • Klouček, P.1    Luskin, M.2
  • 18
    • 0000635099 scopus 로고    scopus 로고
    • Numerical approach to double well problems
    • M. KRUŽÍK, Numerical approach to double well problems, SIAM J. Numer. Anal., 35 (1998), pp. 1833-1849.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 1833-1849
    • Kružík, M.1
  • 19
    • 0040170655 scopus 로고    scopus 로고
    • Finite element analysis of microstructure for the cubic to tetragonal transformation
    • B. LI AND M. LUSKIN, Finite element analysis of microstructure for the cubic to tetragonal transformation, SIAM J. Numer. Anal., 35 (1998), pp. 376-392.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 376-392
    • Li, B.1    Luskin, M.2
  • 20
    • 0032364336 scopus 로고    scopus 로고
    • Nonconforming finite element approximation of crystalline microstructure
    • B. LI AND M. LUSKIN, Nonconforming finite element approximation of crystalline microstructure, Math. Comp., 67 (1998), pp. 917-946.
    • (1998) Math. Comp. , vol.67 , pp. 917-946
    • Li, B.1    Luskin, M.2
  • 21
    • 0030353296 scopus 로고    scopus 로고
    • Approximation of a laminated micro structure for a rotationally invariant, double well energy density
    • M. LUSKIN, Approximation of a laminated micro structure for a rotationally invariant, double well energy density, Numer. Math., 75 (1996), pp. 205-221.
    • (1996) Numer. Math. , vol.75 , pp. 205-221
    • Luskin, M.1
  • 22
    • 0347284844 scopus 로고    scopus 로고
    • On the computation of crystalline microstructure
    • M. LUSKIN, On the computation of crystalline microstructure, Acta Numerica, 5 (1996), pp. 191-257.
    • (1996) Acta Numerica , vol.5 , pp. 191-257
    • Luskin, M.1
  • 23
    • 0042741583 scopus 로고    scopus 로고
    • An adaptive finite element method for solving a double well problem describing crystalline microstructure
    • to appear
    • A. PROHL, An adaptive finite element method for solving a double well problem describing crystalline microstructure, RAIRO Modél. Math. Anal. Numér., to appear.
    • RAIRO Modél. Math. Anal. Numér.
    • Prohl, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.