메뉴 건너뛰기




Volumn 13, Issue 3, 2003, Pages 373-393

Approximation by piecewise constant functions in a BV metric

Author keywords

Approximation; Bounded variation; Finite element; Martensite; Piecewise constant; Thin film

Indexed keywords


EID: 0037357291     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202503002556     Document Type: Article
Times cited : (13)

References (33)
  • 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) 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, Phil. Trans. R. Soc. London A338 (1992) 389-450.
    • (1992) Phil. Trans. R. Soc. London , vol.A338 , pp. 389-450
    • Ball, J.1    James, R.2
  • 4
    • 0033437538 scopus 로고    scopus 로고
    • The simply laminated microstructure in martensitic crystals that undergo a cubic to orthorhombic phase transformation
    • K. Bhattacharya, B. Li and M. Luskin, The simply laminated microstructure in martensitic crystals that undergo a cubic to orthorhombic phase transformation, Arch. Rational Mech. Anal. 149 (1999) 123-154.
    • (1999) Arch. Rational Mech. Anal. , vol.149 , pp. 123-154
    • Bhattacharya, K.1    Li, B.2    Luskin, M.3
  • 6
    • 0035606872 scopus 로고    scopus 로고
    • On the numerical modeling of deformations of pressurized martensitic thin films
    • P. Bělík, T. Brule and M. Luskin, On the numerical modeling of deformations of pressurized martensitic thin films, Math. Model. Numer. Anal. 35 (2001) 525-548.
    • (2001) Math. Model. Numer. Anal. , vol.35 , pp. 525-548
    • Bělík, P.1    Brule, T.2    Luskin, M.3
  • 7
    • 0034396221 scopus 로고    scopus 로고
    • Stability of microstructure for tetragonal to monoclinic martensitic transformations
    • P. Bělík and M. Luskin, Stability of microstructure for tetragonal to monoclinic martensitic transformations, Math. Model. Numer. Anal. 34 (2000) 663-685.
    • (2000) Math. Model. Numer. Anal. , vol.34 , pp. 663-685
    • Bělík, P.1    Luskin, M.2
  • 8
    • 0036721980 scopus 로고    scopus 로고
    • A computational model for the indentation and phase transformation of a martensitic thin film
    • P. Bělík and M. Luskin, A computational model for the indentation and phase transformation of a martensitic thin film, J. Mech. Phys. Solids 50 (2002) 1789-1815.
    • (2002) J. Mech. Phys. Solids , vol.50 , pp. 1789-1815
    • Bělík, P.1    Luskin, M.2
  • 9
    • 0002572859 scopus 로고    scopus 로고
    • A total-variation surface energy model for thin films of martensitic crystals
    • P. Bělík and M. Luskin, A total-variation surface energy model for thin films of martensitic crystals, Interfaces and Free Boundaries 4 (2002) 71-88.
    • (2002) Interfaces and Free Boundaries , vol.4 , pp. 71-88
    • Bělík, P.1    Luskin, M.2
  • 10
    • 0000088421 scopus 로고    scopus 로고
    • Numerical analysis of compatible phase transitions in elastic solids
    • C. Carstensen and P. Plecháč, Numerical analysis of compatible phase transitions in elastic solids, SIAM J. Numer. Anal. 37 (2000) 2061-2081.
    • (2000) SIAM J. Numer. Anal. , vol.37 , pp. 2061-2081
    • Carstensen, C.1    Plecháč, P.2
  • 11
    • 0033181496 scopus 로고    scopus 로고
    • Regularization by functions of bounded variation and applications to image enhancement
    • E. Casas, K. Kunisch and C. Pola, Regularization by functions of bounded variation and applications to image enhancement, Appl. Math. Optim. 40 (1999) 229-257.
    • (1999) Appl. Math. Optim. , vol.40 , pp. 229-257
    • Casas, E.1    Kunisch, K.2    Pola, C.3
  • 12
    • 21844504886 scopus 로고
    • Numerical analysis of oscillations in multiple well problems
    • M. Chipot, C. Collins and D. Kinderlehrer, Numerical analysis of oscillations in multiple well problems, Numer. Math. 70 (1995) 259-282.
    • (1995) Numer. Math. , vol.70 , pp. 259-282
    • Chipot, M.1    Collins, C.2    Kinderlehrer, D.3
  • 14
    • 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) 1271-1298.
    • (1998) SIAM. J. Numer. Anal , vol.35 , pp. 1271-1298
    • Collins, C.1
  • 15
    • 0000427927 scopus 로고    scopus 로고
    • Convergence of an iterative method for total variation denoising
    • D. C. Dobson and C. R. Vogel, Convergence of an iterative method for total variation denoising, SIAM J. Numer. Anal. 34 (1997) 1779-1791.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 1779-1791
    • Dobson, D.C.1    Vogel, C.R.2
  • 17
    • 0031275313 scopus 로고    scopus 로고
    • On approximation in total variation penalization for image reconstruction and inverse problems
    • B. G. Fitzpatrick and S. L. Keeling, On approximation in total variation penalization for image reconstruction and inverse problems, Numer. Funct. Anal. Optim. 18 (1997) 941-958.
    • (1997) Numer. Funct. Anal. Optim. , vol.18 , pp. 941-958
    • Fitzpatrick, B.G.1    Keeling, S.L.2
  • 18
    • 0000587794 scopus 로고
    • Phase transitions of elastic solid materials
    • I. Fonseca, Phase transitions of elastic solid materials, Arch. Rational Mech. Anal. 107 (1989) 195-223.
    • (1989) Arch. Rational Mech. Anal. , vol.107 , pp. 195-223
    • Fonseca, I.1
  • 20
    • 0003257384 scopus 로고    scopus 로고
    • A discontinuous finite element method for solving a multiwell problem
    • M. Gobbert and A. Prohl, A discontinuous finite element method for solving a multiwell problem, SIAM J. Numer. Anal. 37 (1999) 246-268.
    • (1999) SIAM J. Numer. Anal. , vol.37 , pp. 246-268
    • Gobbert, M.1    Prohl, A.2
  • 21
    • 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) 1833-1849.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 1833-1849
    • Kružík, M.1
  • 22
    • 0035545013 scopus 로고    scopus 로고
    • Young measure approximation in micromagnetics
    • M. Kružík and A. Prohl, Young measure approximation in micromagnetics, Numer. Math. 90 (2001) 291-307.
    • (2001) Numer. Math. , vol.90 , pp. 291-307
    • Kružík, M.1    Prohl, A.2
  • 23
    • 0037084425 scopus 로고    scopus 로고
    • Approximation of martensitic microstructure with general homogeneous boundary data
    • B. Li, Approximation of martensitic microstructure with general homogeneous boundary data, J. Math. Anal. Appl. 266 (2002) 451-467.
    • (2002) J. Math. Anal. Appl. , vol.266 , pp. 451-467
    • Li, B.1
  • 24
    • 0012874940 scopus 로고    scopus 로고
    • Finite element analysis of a class of stress-free martensitic microstructures
    • to appear
    • B. Li, Finite element analysis of a class of stress-free martensitic microstructures, Math. Comp., to appear.
    • Math. Comp.
    • Li, B.1
  • 25
    • 0031322111 scopus 로고    scopus 로고
    • Simultaneous numerical approximation of microstructures and relaxed minimizers
    • Z. Li, Simultaneous numerical approximation of microstructures and relaxed minimizers, Numer. Math. 78 (1997) 21-38.
    • (1997) Numer. Math. , vol.78 , pp. 21-38
    • Li, Z.1
  • 26
    • 0032345755 scopus 로고    scopus 로고
    • Rotational transformation method and some numerical techniques for computing microstructures
    • Z. Li, Rotational transformation method and some numerical techniques for computing microstructures, Math. Models Methods Appl. Sci. 8 (1998) 985-1002.
    • (1998) Math. Models Methods Appl. Sci. , vol.8 , pp. 985-1002
    • Li, Z.1
  • 27
    • 0347284844 scopus 로고    scopus 로고
    • On the computation of crystalline microstructure
    • M. Luskin, On the computation of crystalline microstructure, Acta Numerica 5 (1996) 191-258.
    • (1996) Acta Numerica , vol.5 , pp. 191-258
    • Luskin, M.1
  • 28
    • 0030353296 scopus 로고    scopus 로고
    • Approximation of a laminated microstructure for a rotationally invariant, double well energy density
    • M. Luskin, Approximation of a laminated microstructure for a rotationally invariant, double well energy density, Numer. Math. 75 (1997) 205-221.
    • (1997) Numer. Math. , vol.75 , pp. 205-221
    • Luskin, M.1
  • 29
    • 0012892488 scopus 로고    scopus 로고
    • Computational modeling of microstructure
    • ICM 2002, Beijing
    • M. Luskin, Computational modeling of microstructure, in Proc. of the Int. Congress of Mathematicians, ICM 2002, Beijing, Vol. III (2002) 707-716.
    • (2002) Proc. of the Int. Congress of Mathematicians , vol.3 , pp. 707-716
    • Luskin, M.1
  • 30
    • 0026843542 scopus 로고
    • Analysis of the finite element approximation of microstructure in micromagnetics
    • M. Luskin and L. Ma, Analysis of the finite element approximation of microstructure in micromagnetics, SIAM J. Numer. Anal. 29 (1992) 320-331.
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 320-331
    • Luskin, M.1    Ma, L.2
  • 31
    • 0036795283 scopus 로고    scopus 로고
    • Visco-elasto-plastic model for martensitic phase transformation in shape-memory alloys
    • P. Plecháč and T.Roubíček, Visco-elasto-plastic model for martensitic phase transformation in shape-memory alloys, Math. Methods Appl. Sci. 25 (2002) 1281-1298.
    • (2002) Math. Methods Appl. Sci. , vol.25 , pp. 1281-1298
    • Plecháč, P.1    Roubíček, T.2
  • 32
    • 0033421742 scopus 로고    scopus 로고
    • An adaptive finite element method for solving a double well problem describing crystalline microstructure
    • A. Prohl, An adaptive finite element method for solving a double well problem describing crystalline microstructure, Math. Model. Numer. Anal. 33 (1999) 781-796.
    • (1999) Math. Model. Numer. Anal. , vol.33 , pp. 781-796
    • Prohl, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.