메뉴 건너뛰기




Volumn 89, Issue 3, 2001, Pages 425-444

Numerical approximation of non-homogeneous, non-convex vector variational problems

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0035629715     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00005473     Document Type: Article
Times cited : (5)

References (39)
  • 1
    • 0041128262 scopus 로고    scopus 로고
    • On the computation of the rank-one convex hull
    • accepted
    • Aranda, E., Pedregal, P., (2000): On the computation of the rank-one convex hull. SIAM J. Sci. Comput., (accepted)
    • (2000) SIAM J. Sci. Comput.
    • Aranda, E.1    Pedregal, P.2
  • 3
    • 33750297145 scopus 로고
    • Fine phase mixtures as minimizers of energy
    • Ball, J.M., James, R.D., (1987): Fine phase mixtures as minimizers of energy. Arch. Rational Mech. Anal. 100, 13-52
    • (1987) Arch. Rational Mech. Anal. , vol.100 , pp. 13-52
    • Ball, J.M.1    James, R.D.2
  • 4
    • 0002854369 scopus 로고
    • Proposed experimental tests of a theory of fine microstructure and the two-well problem
    • Ball, J.M., James, R.D., (1992): Proposed experimental tests of a theory of fine microstructure and the two-well problem. Phil. Trans. R. Soc. London A 338, 389-450
    • (1992) Phil. Trans. R. Soc. London A , vol.338 , pp. 389-450
    • Ball, J.M.1    James, R.D.2
  • 7
    • 0031533725 scopus 로고    scopus 로고
    • Numerical solution of the scalar double-well problem allowing microstructure
    • Carstensen, C., Plecháč, P., (1997): Numerical solution of the scalar double-well problem allowing microstructure. Math. Comp. 66(219), 997-1026
    • (1997) Math. Comp. , vol.66 , Issue.219 , pp. 997-1026
    • Carstensen, C.1    Plecháč, P.2
  • 9
    • 0001006601 scopus 로고
    • Numerical analysis of oscillations in nonconvex problems
    • Chipot, M., (1991): Numerical analysis of oscillations in nonconvex problems. Numer. Math. 59, 747-767
    • (1991) Numer. Math. , vol.59 , pp. 747-767
    • Chipot, M.1
  • 10
    • 0033460991 scopus 로고    scopus 로고
    • The appearance of microstructures in problems with incompatible wells and their numerical approach
    • Chipot, M., (1999): The appearance of microstructures in problems with incompatible wells and their numerical approach. Numer. Math. 83, 325-352
    • (1999) Numer. Math. , vol.83 , pp. 325-352
    • Chipot, M.1
  • 11
    • 0026907665 scopus 로고
    • Numerical approximation in variational problems with potential wells
    • Chipot, M., Collins, C., (1992): Numerical approximation in variational problems with potential wells SIAM J. Numer. Anal. 29(4), 1002-1019
    • (1992) SIAM J. Numer. Anal. , vol.29 , Issue.4 , pp. 1002-1019
    • Chipot, M.1    Collins, C.2
  • 15
    • 0001800199 scopus 로고
    • Computation of twinning
    • Luskin, M., Kinderlehrer, D., James, R., Ericksen, J.L., editors. Berlin Heidelberg New York: Springer
    • Collins, C., (1993): Computation of twinning. In Luskin, M., Kinderlehrer, D., James, R., Ericksen, J.L., editors, Microstructure and Phase Transition, volume 54 of IMA Volumes, 39-50. Berlin Heidelberg New York: Springer
    • (1993) Microstructure and Phase Transition, Volume 54 of IMA Volumes , vol.54 , pp. 39-50
    • Collins, C.1
  • 16
    • 0026136907 scopus 로고
    • Numerical approximation of the solution of a variational problem with a double well potential
    • Collins, C., Kinderlehrer, D., Luskin, M, (1991): Numerical approximation of the solution of a variational problem with a double well potential. SIAM J. Numer. Anal. 28(2), 321-332
    • (1991) SIAM J. Numer. Anal. , vol.28 , Issue.2 , pp. 321-332
    • Collins, C.1    Kinderlehrer, D.2    Luskin, M.3
  • 17
    • 84966255684 scopus 로고
    • Optimal order error estimate for the finite element approximation of the solution of a nonconvex variational problem
    • Collins, C., Luskin, M., (1991): Optimal order error estimate for the finite element approximation of the solution of a nonconvex variational problem. Math. Comp. 57, 621-637
    • (1991) Math. Comp. , vol.57 , pp. 621-637
    • Collins, C.1    Luskin, M.2
  • 18
    • 0001830197 scopus 로고
    • Computational results for a two-dimensional model of crystalline microstructure
    • Luskin, M., Kinderlehrer, D., James, R., Ericksen, J.L., editors. Berlin Heidelberg New York: Springer
    • Collins, C., Luskin, M., Riordan, J., (1993): Computational results for a two-dimensional model of crystalline microstructure. In Luskin, M., Kinderlehrer, D., James, R., Ericksen, J.L., editors, Microstructure and Phase Transition, volume 54 of IMA Volumes, 51-57. Berlin Heidelberg New York: Springer
    • (1993) Microstructure and Phase Transition, Volume 54 of IMA Volumes , vol.54 , pp. 51-57
    • Collins, C.1    Luskin, M.2    Riordan, J.3
  • 19
    • 0000760712 scopus 로고
    • Remarques sur les notions de polyconvexité, quasi-convexité et convexité de rang 1
    • Dacorogna, B., (1985): Remarques sur les notions de polyconvexité, quasi-convexité et convexité de rang 1. J. Math. Pures Appl. 64, 403-438
    • (1985) J. Math. Pures Appl. , vol.64 , pp. 403-438
    • Dacorogna, B.1
  • 21
    • 0022906928 scopus 로고
    • Constitutive theory for some constrained elastic crystals
    • Ericksen, J.L., (1986): Constitutive theory for some constrained elastic crystals. Int. J. Solids and Structures 22, 951-964
    • (1986) Int. J. Solids and Structures , vol.22 , pp. 951-964
    • Ericksen, J.L.1
  • 23
    • 0000170338 scopus 로고
    • Blowup, compactness and partial regularity in the calculus of variations
    • Evans, L.C., Gariepy, R.F., (1987): Blowup, compactness and partial regularity in the calculus of variations. Ind. Univ. Math. J. 36(2), 361-371
    • (1987) Ind. Univ. Math. J. , vol.36 , Issue.2 , pp. 361-371
    • Evans, L.C.1    Gariepy, R.F.2
  • 24
    • 84976128757 scopus 로고
    • Some remarks concerning quasiconvexity and strong convergence
    • Evans, L.C., Gariepy, R.F., (1987): Some remarks concerning quasiconvexity and strong convergence. Proc. R. Soc. Edinburgh Sect. A. 106, 53-61
    • (1987) Proc. R. Soc. Edinburgh Sect. A. , vol.106 , pp. 53-61
    • Evans, L.C.1    Gariepy, R.F.2
  • 25
    • 0023142918 scopus 로고
    • Variational methods for elastic crystals
    • Fonseca, I., (1985): Variational methods for elastic crystals. Arch. Rational Mech. Anal. 97, 189-220
    • (1985) Arch. Rational Mech. Anal. , vol.97 , pp. 189-220
    • Fonseca, I.1
  • 26
    • 0002413112 scopus 로고
    • Extension and selection theorems in topological spaces with a generalized convexity structure
    • Horvath, C.D., (1993): Extension and selection theorems in topological spaces with a generalized convexity structure. Annales de la Faculté des Sciences de Toulouse II(2), 253-269
    • (1993) Annales de la Faculté des Sciences de Toulouse , vol.2 , Issue.2 , pp. 253-269
    • Horvath, C.D.1
  • 27
  • 28
    • 0001000267 scopus 로고
    • The relaxation of a double-well energy
    • Kohn, R.V., (1991): The relaxation of a double-well energy. Cont. Mech. Thermodyn. 3, 193-236
    • (1991) Cont. Mech. Thermodyn. , vol.3 , pp. 193-236
    • Kohn, R.V.1
  • 30
    • 0347284844 scopus 로고    scopus 로고
    • On the computation of crystalline microstructure
    • Luskin, M., (1996): On the computation of crystalline microstructure. Acta Numerica 5, 191-257
    • (1996) Acta Numerica , vol.5 , pp. 191-257
    • Luskin, M.1
  • 31
    • 0039941403 scopus 로고
    • Minimizing sequences for non-convex functional, phase transitions and singular perturbations
    • Berlin Heidelberg New York: Springer
    • Müller, S., (1990): Minimizing sequences for non-convex functional, phase transitions and singular perturbations. In Problems Involving Change of Type, Lecture Notes in Physics, 31-44. Berlin Heidelberg New York: Springer
    • (1990) Problems Involving Change of Type, Lecture Notes in Physics , pp. 31-44
    • Müller, S.1
  • 32
    • 0000658988 scopus 로고
    • Computation of microstructure utilizing young measure representations
    • C.A. Rogers and R.A. Rogers, editors. Technomic Publishing Co., Lancaster
    • Nicolaides, R.A., Walkington, N.J., (1992): Computation of microstructure utilizing young measure representations. In C.A. Rogers and R.A. Rogers, editors. Recent Advances in Adaptative and Sensory Materials and their Applications, 131-141 Technomic Publishing Co., Lancaster
    • (1992) Recent Advances in Adaptative and Sensory Materials and Their Applications , pp. 131-141
    • Nicolaides, R.A.1    Walkington, N.J.2
  • 33
    • 0031173550 scopus 로고    scopus 로고
    • Numerical methods for a nonconvex optimization problem modeling martensitic microstructure
    • Nicolaides, R.A., Walkington, N.J., Wang, H., (1997): Numerical methods for a nonconvex optimization problem modeling martensitic microstructure. SIAM J. Sci. Comput. 18(4), 1122-1141
    • (1997) SIAM J. Sci. Comput. , vol.18 , Issue.4 , pp. 1122-1141
    • Nicolaides, R.A.1    Walkington, N.J.2    Wang, H.3
  • 34
    • 0000521811 scopus 로고
    • Laminates and microstucture
    • Pedregal, P., (1993): Laminates and microstucture. Eur. J. Appl. Math. 4, 121-149
    • (1993) Eur. J. Appl. Math. , vol.4 , pp. 121-149
    • Pedregal, P.1
  • 35
    • 0000572269 scopus 로고
    • Numerical approximation of parametrized measures
    • Pedregal, P., (1995): Numerical approximation of parametrized measures. Numer. Fund. Anal. Optimiz. 16(7&8), 1049-1062
    • (1995) Numer. Fund. Anal. Optimiz. , vol.16 , Issue.7-8 , pp. 1049-1062
    • Pedregal, P.1
  • 36
    • 0030508310 scopus 로고    scopus 로고
    • On the numerical analysis of non-convex variational problems
    • Pedregal, P., (1996): On the numerical analysis of non-convex variational problems. Numer. Math. 74, 325-336
    • (1996) Numer. Math. , vol.74 , pp. 325-336
    • Pedregal, P.1
  • 38
    • 0001682439 scopus 로고
    • On the problem of two wells
    • D. Kinderlehrer et al., editor. Berlin Heidelberg New York: Springer
    • Šverák, V., (1992): On the problem of two wells. In D. Kinderlehrer et al., editor, Microstructure and Phase Transition. Berlin Heidelberg New York: Springer
    • (1992) Microstructure and Phase Transition
    • Šverák, V.1
  • 39
    • 84974157879 scopus 로고
    • Rank-one convexity does not imply quasiconvexity
    • Šverák, V., (1992): Rank-one convexity does not imply quasiconvexity. Proc. R. Soc. Edinburgh Sect. A. 120, 185-189
    • (1992) Proc. R. Soc. Edinburgh Sect. A. , vol.120 , pp. 185-189
    • Šverák, V.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.