메뉴 건너뛰기




Volumn 21, Issue 2, 2011, Pages 491-516

Obstacle problems with cohesion: A hemivariational inequality approach and its efficient numerical solution

Author keywords

Generalized complementarity problem; Generalized Newton method; Hemivariational inequality; Nonsmooth optimization; Obstacle problem with cohesion; Primal dual active set algorithm

Indexed keywords

COMPLEMENTARITY PROBLEMS; GENERALIZED NEWTON METHOD; HEMIVARIATIONAL INEQUALITY; NONSMOOTH OPTIMIZATION; OBSTACLE PROBLEMS; PRIMAL-DUAL;

EID: 79960584035     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/10078299     Document Type: Article
Times cited : (48)

References (45)
  • 3
    • 1142276240 scopus 로고    scopus 로고
    • An iterative solution procedure for winkler-type contact problems with friction
    • T. A. ANGELOV AND A. A. LIOLIOS, An iterative solution procedure for Winkler-type contact problems with friction, ZAMM Z. Angew. Math. Mech., 84 (2004), pp. 136-143.
    • (2004) ZAMM Z. Angew. Math. Mech. , vol.84 , pp. 136-143
    • Angelov, T.A.1    Liolios, A.A.2
  • 4
    • 79551694695 scopus 로고    scopus 로고
    • Indentation of a punch with a fine-grained base into an elastic foundation
    • DOI 10.1023/B:JAMT.0000037976.61963.b6
    • I. I. ARGATOV, Indentation of a punch with a fine-grained base into an elastic foundation, J. Appl. Mech. Tech. Phys., 45 (2004), pp. 764-773. (Pubitemid 39064595)
    • (2004) J. Appl. Mech. Tech. Phys. , vol.45 , Issue.5 , pp. 764-773
    • Argatov, I.I.1
  • 5
    • 4143060521 scopus 로고    scopus 로고
    • Spherical indentation of freestanding circular thin films in the membrane regime
    • M. R. BEGLEY AND T. J. MACKIN, Spherical indentation of freestanding circular thin films in the membrane regime, J. Mech. Phys. Solids, 52 (2004), pp. 2005-2023.
    • (2004) J. Mech. Phys. Solids , vol.52 , pp. 2005-2023
    • Begley, M.R.1    Mackin, T.J.2
  • 6
    • 34548069658 scopus 로고    scopus 로고
    • Convergence analysis of a conforming adaptive finite element method for an obstacle problem
    • C. CARSTENSEN, D. BRAESS, AND R. H. W. HOPPE, Convergence analysis of a conforming adaptive finite element method for an obstacle problem, J. Numer. Math., 107 (2007), pp. 455-471.
    • (2007) J. Numer. Math. , vol.107 , pp. 455-471
    • Carstensen, C.1    Braess, D.2    Hoppe, R.H.W.3
  • 7
    • 0034432264 scopus 로고    scopus 로고
    • Smoothing methods and semismooth methods for nondifferentiable operator equations
    • PII S0036142999356719
    • X. CHEN, Z. NASHED, AND L. QI, Smoothing methods and semi-smooth methods for nondifferentiable operator equations, SIAM J. Numer. Anal., 38 (2000), pp. 1200-1216. (Pubitemid 33778998)
    • (2000) SIAM Journal on Numerical Analysis , vol.38 , Issue.4 , pp. 1200-1216
    • Chen, X.1    Nashed, Z.2    Qi, L.3
  • 9
    • 0036003392 scopus 로고    scopus 로고
    • Mixed finite element methods for unilateral problems: Convergence analysis and numerical studies
    • P. COOREVITS, P. HILD, K. LHALOUANI, AND T. SASSI, Mixed finite element methods for unilateral problems: Convergence analysis and numerical studies, Math. Comp., 71 (2002), pp. 1-25.
    • (2002) Math. Comp. , vol.71 , pp. 1-25
    • Coorevits, P.1    Hild, P.2    Lhalouani, K.3    Sassi, T.4
  • 15
    • 0041657515 scopus 로고    scopus 로고
    • The primal-dual active set strategy as a semismooth Newton method
    • DOI 10.1137/S1052623401383558, PII S1052623401383558
    • M. HINTERMÜLLER, K. ITO, AND K. KUNISCH, The primal-dual active set strategy as a semismooth Newton method, SIAM J. Optim., 13 (2003), pp. 865-888. (Pubitemid 36971115)
    • (2003) SIAM Journal on Optimization , vol.13 , Issue.3 , pp. 865-888
    • Hintermuller, M.1    Ito, K.2    Kunisch, K.3
  • 16
    • 25444510327 scopus 로고    scopus 로고
    • Semismooth newton methods for a class of unilaterally constrained variational problems
    • M. HINTERMÜLLER, V. A. KOVTUNENKO, AND K. KUNISCH, Semismooth Newton methods for a class of unilaterally constrained variational problems, Adv. Math. Sci. Appl., 14 (2004), pp. 513-535.
    • (2004) Adv. Math. Sci. Appl. , vol.14 , pp. 513-535
    • Hintermüller, M.1    Kovtunenko, V.A.2    Kunisch, K.3
  • 17
    • 35448986030 scopus 로고    scopus 로고
    • Constrained optimization for interface cracks in composite materials subject to non-penetration conditions
    • DOI 10.1007/s10665-006-9113-7
    • M. HINTERMÜLLER, V. A. KOVTUNENKO, AND K. KUNISCH, Constrained optimization for interface cracks in composite materials subject to non-penetration conditions, J. Engrg. Math., 59 (2007), pp. 301-321. (Pubitemid 47617498)
    • (2007) Journal of Engineering Mathematics , vol.59 , Issue.3 , pp. 301-321
    • Hintermuller, M.1    Kovtunenko, V.A.2    Kunisch, K.3
  • 18
    • 33847157898 scopus 로고    scopus 로고
    • Path-following methods for a class of constrained minimization problems in function space
    • M. HINTERMÜLLER AND K. KUNISCH, Path-following methods for a class of constrained minimization problems in function space, SIAM J. Optim., 17 (2006), pp. 159-187.
    • (2006) SIAM J. Optim. , vol.17 , pp. 159-187
    • Hintermüller, M.1    Kunisch, K.2
  • 19
    • 33744492592 scopus 로고    scopus 로고
    • A posteriori error estimates for adaptive finite element discretizations of boundary control problems
    • DOI 10.1163/156939506776382139
    • R. H. W. HOPPE, Y. ILIASH, C. IYYUNNI, AND N. H. SWEILAM, A posteriori error estimates for adaptive finite element discretizations of boundary control problem, J. Numer. Math., 14 (2006), pp. 57-82. (Pubitemid 43799653)
    • (2006) Journal of Numerical Mathematics , vol.14 , Issue.1 , pp. 57-82
    • Hoppe, R.H.W.1    Iliash, Y.2    Iyyunni, C.3    Sweilam, N.H.4
  • 20
    • 20444492850 scopus 로고    scopus 로고
    • A priori error estimates and an inexact primal-dual active set strategy for linear and quadratic finite elements applied to multibody contact problems
    • DOI 10.1016/j.apnum.2004.09.019, PII S0168927404001953, Selected papers from the 16th Chemnitz Finite Element Symposium 2003
    • S. HÜEBER, M. MAIR, AND B. WOHLMUTH, A priori error estimates and an inexact primal-dual active set strategy for linear and quadratic finite elements applied to multibody contact problems, Appl. Numer. Math., 54 (2005), pp. 555-576. (Pubitemid 40819673)
    • (2005) Applied Numerical Mathematics , vol.54 , Issue.3-4 , pp. 555-576
    • Hueber, S.1    Mair, M.2    Wohlmuth, B.I.3
  • 21
    • 44749092903 scopus 로고    scopus 로고
    • A primal-dual active set algorithm for three-dimensional contact problems with coulomb friction
    • S. HÜEBER, G. STADLER, AND B. I. WOHLMUTH, A primal-dual active set algorithm for three-dimensional contact problems with Coulomb friction, SIAM J. Sci. Comput., 30 (2008), pp. 572-596.
    • (2008) SIAM J. Sci. Comput. , vol.30 , pp. 572-596
    • Hüeber, S.1    Stadler, G.2    Wohlmuth, B.I.3
  • 22
    • 0003053237 scopus 로고
    • An augmented lagrangian technique for variational inequalities
    • K. ITO AND K. KUNISCH, An augmented Lagrangian technique for variational inequalities, Appl. Math. Optim., 21 (1990), pp. 223-241.
    • (1990) Appl. Math. Optim. , vol.21 , pp. 223-241
    • Ito, K.1    Kunisch, K.2
  • 23
    • 0037261943 scopus 로고    scopus 로고
    • Semi-smooth Newton methods for variational inequalities of the first kind
    • DOI 10.1051/m2an:2003021
    • K. ITO AND K. KUNISCH, Semi-smooth Newton methods for the variational inequalities of the first kind, ESAIM: Math. Model. Numer. Anal., 37 (2003), pp. 41-62. (Pubitemid 36446154)
    • (2003) Mathematical Modelling and Numerical Analysis , vol.37 , Issue.1 , pp. 41-62
    • Ito, K.1    Kunisch, K.2
  • 28
    • 0003295459 scopus 로고
    • An introduction to variational inequalities and their applications
    • Academic Press, New York
    • D. KINDERLEHRER AND G. STAMPACCHIA, An Introduction to Variational Inequalities and Their Applications, Pure and Applied Mathematics, 88, Academic Press, New York, 1980.
    • (1980) Pure and Applied Mathematics , vol.88
    • Kinderlehrer, D.1    Stampacchia, G.2
  • 31
    • 33748999254 scopus 로고    scopus 로고
    • Primal-dual sensitivity analysis of active sets for mixed boundary-value contact problems
    • V. A. KOVTUNENKO, Primal-dual sensitivity analysis of active sets for mixed boundary-value contact problems, J. Engrg. Math., 55 (2006), pp. 151-166.
    • (2006) J. Engrg. Math. , vol.55 , pp. 151-166
    • Kovtunenko, V.A.1
  • 32
    • 33748560077 scopus 로고    scopus 로고
    • Optimization formulation of the evolutionary problem of crack propagation under quasibrittle fracture
    • DOI 10.1007/s10808-006-0107-z
    • V. A. KOVTUNENKO AND I. V. SUKHORUKOV, Optimization formulation of the evolutionary problem of crack propagation under quasibrittle fracture, J. Appl. Mech. Tech. Phys., 47 (2006), pp. 704-713. (Pubitemid 44363702)
    • (2006) Journal of Applied Mechanics and Technical Physics , vol.47 , Issue.5 , pp. 704-713
    • Kovtunenko, V.A.1    Sukhorukov, I.V.2
  • 33
    • 77953948236 scopus 로고    scopus 로고
    • Variational and quasivariational inequations in mechanics
    • Springer, Dordrecht
    • A. S. KRAVCHUK AND P. J. NEITTAANMAKI, Variational and Quasivariational Inequations in Mechanics, Solid Mech. Appl. 147, Springer, Dordrecht, 2007.
    • (2007) Solid Mech. Appl. , vol.147
    • Kravchuk, A.S.1    Neittaanmaki, P.J.2
  • 34
    • 2942525310 scopus 로고    scopus 로고
    • Initiation and propagation of fracture in the models of Griffith and Barenblatt
    • DOI 10.1007/s00161-003-0164-y
    • J.-J. MARIGO AND L. TRUSKINOVSKY, Initiation and propagation of fracture in the models of Griffith and Barenblatt, Contin. Mech. Thermodyn., 16 (2004), pp. 391-409. (Pubitemid 38739669)
    • (2004) Continuum Mechanics and Thermodynamics , vol.16 , Issue.4 , pp. 391-409
    • Marigo, J.-J.1    Truskinovsky, L.2
  • 36
    • 0036959161 scopus 로고    scopus 로고
    • Convergence of adaptive finite element methods
    • P. MORIN, R. H. NOCHETTO, AND K. G. SIEBERT, Convergence of adaptive finite element methods, SIAM Rev., 44 (2002), pp. 631-658.
    • (2002) SIAM Rev. , vol.44 , pp. 631-658
    • Morin, P.1    Nochetto, R.H.2    Siebert, K.G.3
  • 39
    • 0041411640 scopus 로고    scopus 로고
    • Pointwise a posteriori error control for elliptic obstacle problems
    • DOI 10.1007/s00211-002-0411-3
    • R. H. NOCHETTO, K. G. SIEBERT, AND A. VEESER, Pointwise a posteriori error control for elliptic obstacle problems, Numer. Math., 95 (2003), pp. 163-195. (Pubitemid 36914033)
    • (2003) Numerische Mathematik , vol.95 , Issue.1 , pp. 163-195
    • Nochetto, R.H.1    Siebert, K.G.2    Veeser, A.3
  • 40
    • 0345504743 scopus 로고    scopus 로고
    • A consistent model coupling adhesion, friction, and unilateral contact
    • M. RAOUS, L. CANGÉMI, AND M. COCU, A consistent model coupling adhesion, friction, and unilateral contact, Comput. Methods Appl. Mech. Engrg., 177 (1999), pp. 383-399.
    • (1999) Comput. Methods Appl. Mech. Engrg. , vol.177 , pp. 383-399
    • Raous, M.1    Cangémi, L.2    Cocu, M.3
  • 42
    • 0003223521 scopus 로고    scopus 로고
    • Obstacle problems in mathematical physics
    • Elsevier, Amsterdam, 1987, Math. Notes 114, Princeton University Press, Princeton, NJ
    • J.-F. RODRIGUES, Obstacle Problems in Mathematical Physics, North-Holland Math. Studies 134, Elsevier, Amsterdam, 1987, Math. Notes 114, Princeton University Press, Princeton, NJ.
    • North-holland Math. Studies , vol.134
    • Rodrigues, J.-F.1
  • 43
    • 64249153666 scopus 로고    scopus 로고
    • Local minima of quadratic forms on convex cones
    • A. SEEGER AND M. TORKI, Local minima of quadratic forms on convex cones, J. Global Optim., 44 (2009), pp. 1-28.
    • (2009) J. Global Optim. , vol.44 , pp. 1-28
    • Seeger, A.1    Torki, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.