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Volumn 66, Issue 219, 1997, Pages 997-1026

Numerical solution of the scalar double-well problem allowing microstructure

Author keywords

Microstructure; Non convex minimisation; Young measures

Indexed keywords


EID: 0031533725     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0025-5718-97-00849-1     Document Type: Article
Times cited : (82)

References (24)
  • 1
    • 0000093666 scopus 로고
    • A version of the fundamental theorem for Young measures
    • M Rascle, D. Serre, and M. Slemrod, editors, MR 91c:19021
    • J.M. Ball, A version of the fundamental theorem for Young measures, In M Rascle, D. Serre, and M. Slemrod, editors, Partial differential equations and continuum models of phase transitions, LNP 344, pages 207 215, 1989. MR 91c:19021
    • (1989) Partial Differential Equations and Continuum Models of Phase Transitions, LNP , vol.344 , pp. 207-215
    • Ball, J.M.1
  • 2
    • 0028379765 scopus 로고
    • Approximated convex envelope of a function
    • MR 94m:49049
    • B. Brighi and M. Chipot, Approximated convex envelope of a function, SIAM J. Numer. Anal., 31, 1994. MR 94m:49049
    • (1994) SIAM J. Numer. Anal. , pp. 31
    • Brighi, B.1    Chipot, M.2
  • 3
    • 33750297145 scopus 로고
    • Fine phase mixtures as minimisers of energy
    • MR 89c:80005
    • J. M. Ball and R. D. James, Fine phase mixtures as minimisers of energy, Arch. Rational Mech. Anal., 100:13-52, 1987. MR 89c:80005
    • (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 the theory of fine microstructure and the two-well problem
    • J. M. Ball and R. D. James, Proposed experimental tests of the theory of fine microstructure and the two-well problem, Phil. Trans. R. Soc. Lond. A., 338:389-450, 1992.
    • (1992) Phil. Trans. R. Soc. Lond. A. , vol.338 , pp. 389-450
    • Ball, J.M.1    James, R.D.2
  • 5
    • 34249955899 scopus 로고
    • A nonconvex variational problem related to change of phase
    • MR 90i:49004
    • P. Bauman and D. Phillips, A nonconvex variational problem related to change of phase, Appl. Math. Optimization, 21:113-138, 1990. MR 90i:49004
    • (1990) Appl. Math. Optimization , vol.21 , pp. 113-138
    • Bauman, P.1    Phillips, D.2
  • 7
    • 0026907665 scopus 로고
    • Numerical approximations in variational problems with potential wells
    • MR 93j:65171
    • M. Chipot and C. Collins, Numerical approximations in variational problems with potential wells. SIAM J. Numer. Anal., 29:1002-1019, 1992. MR 93j:65171
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 1002-1019
    • Chipot, M.1    Collins, C.2
  • 8
    • 0001006601 scopus 로고
    • Numerical analysis of oscillations in nonconvex problems
    • MR, 92h:65164
    • M. Chipot, Numerical analysis of oscillations in nonconvex problems, Numer. Math., 59:747-767, 1991. MR, 92h:65164
    • (1991) Numer. Math. , vol.59 , pp. 747-767
    • Chipot, M.1
  • 9
    • 84966255684 scopus 로고
    • Optimal order error estimates for the finite element approximation of a solution of a, nonconvex variational problem
    • MR, 92a:65276
    • C. Collins and M. Luskin, Optimal order error estimates for the finite element approximation of a solution of a, nonconvex variational problem, Math. Comp., 57:621-637, 1991. MR, 92a:65276
    • (1991) Math. Comp. , vol.57 , pp. 621-637
    • Collins, C.1    Luskin, M.2
  • 10
    • 0016541865 scopus 로고
    • Approximation by finite element functions using local regularization
    • MR 53:4569
    • P. Clement, Approximation by finite element functions using local regularization, RAIRO Sér. Rouge Anal. Numér., R-2:77-84, 1975. MR 53:4569
    • (1975) RAIRO Sér. Rouge Anal. Numér. , vol.R-2 , pp. 77-84
    • Clement, P.1
  • 12
    • 0001139965 scopus 로고
    • Characterisations of young measures generated by gradients
    • MR 92k:49089
    • P. Pedregal D. Kinderlehrer, Characterisations of Young measures generated by gradients, Arch. Rat. Mech. Anal., 115:329-365, 1991. MR 92k:49089
    • (1991) Arch. Rat. Mech. Anal. , vol.115 , pp. 329-365
    • Pedregal, P.1    Kinderlehrer, D.2
  • 14
    • 0025416425 scopus 로고
    • On the convergence of finite element approximations of a relaxed variational problem
    • MR 91f:65167
    • D. French, On the convergence of finite element approximations of a relaxed variational problem, SIAM J. Num. Anal., 27:419-436, 1990. MR 91f:65167
    • (1990) SIAM J. Num. Anal. , vol.27 , pp. 419-436
    • French, D.1
  • 15
    • 84973960437 scopus 로고
    • A necessary and sufficient condition for non-attainment and formation of microstructure almost everywhere in scalar variational problems
    • MR 96g:49001
    • G. Friesecke, A necessary and sufficient condition for non-attainment and formation of microstructure almost everywhere in scalar variational problems, Proc. R. Soc. Edin, 124A:437-471, 1994. MR 96g:49001
    • (1994) Proc. R. Soc. Edin , vol.124 A , pp. 437-471
    • Friesecke, G.1
  • 16
    • 0022766604 scopus 로고
    • Numerical study of a relaxed variational problem from optimal design
    • MR 88a:73054
    • J. Goodman, R. V. Kohn, and L. Reyna, Numerical study of a relaxed variational problem from optimal design, Comput. Methods Appl. Mech. Engrg., 57:107-127, 1986. MR 88a:73054
    • (1986) Comput. Methods Appl. Mech. Engrg. , vol.57 , pp. 107-127
    • Goodman, J.1    Kohn, R.V.2    Reyna, L.3
  • 17
    • 0019556162 scopus 로고
    • On the anti-plane shear problem in elasticity
    • MR 82d:73030
    • M. E. Gurtin and R. Temam, On the anti-plane shear problem in elasticity, J. Elasticity, 11:197-206, 1981. MR 82d:73030
    • (1981) J. Elasticity , vol.11 , pp. 197-206
    • Gurtin, M.E.1    Temam, R.2
  • 18
    • 0003073394 scopus 로고
    • Weak convergence of integrands and the Young measure representation
    • MR 92m:49076
    • D. Kinderlehrer and P. Pedregal, Weak convergence of integrands and the Young measure representation, SIAM J Math. Anal., 23:1 19, 1991. MR 92m:49076
    • (1991) SIAM J Math. Anal. , vol.23 , pp. 1-19
    • Kinderlehrer, D.1    Pedregal, P.2
  • 19
    • 0021481124 scopus 로고
    • Newton-type minimisation via the Lanczos method
    • MR 86h:65092
    • S. Nash, Newton-type minimisation via the Lanczos method, SIAM J. Num. Anal., 21:770-787, 1984. MR 86h:65092
    • (1984) SIAM J. Num. Anal. , vol.21 , pp. 770-787
    • Nash, S.1
  • 20
    • 0000658988 scopus 로고
    • Computation of microstructure utilizing Young measure representations
    • C.A. Rogers and R.A. Rogers, editors, Lancaster, Technomic Publishing Co.
    • R. A. Nicolaides and N. J. Walkington, Computation of microstructure utilizing Young measure representations, In C.A. Rogers and R.A. Rogers, editors, Recent Advances in Adaptive and Sensory Materials and their Applications, pages 131-141, Lancaster, 1992. Technomic Publishing Co.
    • (1992) Recent Advances in Adaptive and Sensory Materials and Their Applications , pp. 131-141
    • Nicolaides, R.A.1    Walkington, N.J.2
  • 21
    • 84968511032 scopus 로고
    • Strong convergence of numerical solutions to degenerate variational problems
    • MR 95m:65183
    • R. A. Nicolaides and N. J. Walkington, Strong convergence of numerical solutions to degenerate variational problems, Math. Comp., 64:117-127, 1995. MR 95m:65183
    • (1995) Math. Comp. , vol.64 , pp. 117-127
    • Nicolaides, R.A.1    Walkington, N.J.2
  • 22
    • 0040718038 scopus 로고
    • Jensen's inequality in calculus of variations
    • MR 94i:49032
    • P. Pedregal, Jensen's inequality in calculus of variations, Differential Integral Equations, 7:57-72, 1994. MR 94i:49032
    • (1994) Differential Integral Equations , vol.7 , pp. 57-72
    • Pedregal, P.1
  • 24
    • 84968521915 scopus 로고
    • A posteriori error estimates for nonlinear problems. Finite element discretization of elliptic equations
    • MR 94j:65136
    • R. Verfürth, A posteriori error estimates for nonlinear problems. Finite element discretization of elliptic equations, Math. Comp., 62:445-475, 1994. MR 94j:65136
    • (1994) Math. Comp. , vol.62 , pp. 445-475
    • Verfürth, R.1


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