메뉴 건너뛰기




Volumn 389, Issue 1, 2012, Pages 618-631

Regularity and Rothe method error estimates for parabolic hemivariational inequality

Author keywords

Clarke subdifferential; Differential inclusion; Error estimates; Hemivariational inequality; Parabolic problem; Regularity; Rothe method

Indexed keywords


EID: 84855829408     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2011.12.007     Document Type: Article
Times cited : (28)

References (42)
  • 2
    • 58149156394 scopus 로고    scopus 로고
    • A frictionless viscoelastodynamic contact problem with energy consistent properties: Numerical analysis and computational aspects
    • Ayyad Y., Barboteu M., Fernàndez J.R. A frictionless viscoelastodynamic contact problem with energy consistent properties: Numerical analysis and computational aspects. Comput. Methods Appl. Mech. Engrg. 2009, 198:669-679.
    • (2009) Comput. Methods Appl. Mech. Engrg. , vol.198 , pp. 669-679
    • Ayyad, Y.1    Barboteu, M.2    Fernàndez, J.R.3
  • 3
    • 0002552584 scopus 로고
    • Discretization of evolution ineqialities
    • Birkhäuser, Boston, F. Colombini, L. Modica, S. Spagnolo (Eds.)
    • Baiocchi C. Discretization of evolution ineqialities. Partial Differential Equations and Calculus of Variations 1989, 59-92. Birkhäuser, Boston. F. Colombini, L. Modica, S. Spagnolo (Eds.).
    • (1989) Partial Differential Equations and Calculus of Variations , pp. 59-92
    • Baiocchi, C.1
  • 4
    • 0036337515 scopus 로고    scopus 로고
    • Numerical precision for differential inclusions with uniqueness
    • Bastien J., Schatzman M. Numerical precision for differential inclusions with uniqueness. ESAIM Math. Model. Numer. Anal. 2002, 36:427-460.
    • (2002) ESAIM Math. Model. Numer. Anal. , vol.36 , pp. 427-460
    • Bastien, J.1    Schatzman, M.2
  • 5
    • 0030526649 scopus 로고    scopus 로고
    • Monotonicity methods for nonlinear evolution equations
    • Berkovits J., Mustonen V. Monotonicity methods for nonlinear evolution equations. Nonlinear Anal. 1996, 27:1397-1405.
    • (1996) Nonlinear Anal. , vol.27 , pp. 1397-1405
    • Berkovits, J.1    Mustonen, V.2
  • 6
    • 0000748768 scopus 로고    scopus 로고
    • Enclosure of solutions for quasilinear dynamic hemivariational inequalities
    • Carl S. Enclosure of solutions for quasilinear dynamic hemivariational inequalities. Nonlinear World 1996, 3:281-298.
    • (1996) Nonlinear World , vol.3 , pp. 281-298
    • Carl, S.1
  • 7
    • 0038626222 scopus 로고    scopus 로고
    • Extremal solutions of quasilinear parabolic inclusions with generalized Clarke's gradient
    • Carl S., Motreanu D. Extremal solutions of quasilinear parabolic inclusions with generalized Clarke's gradient. J. Differential Equations 2003, 191:206-233.
    • (2003) J. Differential Equations , vol.191 , pp. 206-233
    • Carl, S.1    Motreanu, D.2
  • 8
    • 8644274779 scopus 로고    scopus 로고
    • Extremality in solving general quasilinear parabolic inclusions
    • Carl S., Motreanu D. Extremality in solving general quasilinear parabolic inclusions. J. Optim. Theory Appl. 2004, 123:463-477.
    • (2004) J. Optim. Theory Appl. , vol.123 , pp. 463-477
    • Carl, S.1    Motreanu, D.2
  • 9
    • 33745869081 scopus 로고    scopus 로고
    • Existence and comparison results for noncoercive and nonmonotone multivalued elliptic problems
    • Carl S. Existence and comparison results for noncoercive and nonmonotone multivalued elliptic problems. Nonlinear Anal. 2006, 65:1532-1546.
    • (2006) Nonlinear Anal. , vol.65 , pp. 1532-1546
    • Carl, S.1
  • 11
    • 43949131389 scopus 로고    scopus 로고
    • Evolutionary variational-hemivariational inequalities: existence and comparison results
    • Carl S., Le V.K., Motreanu D. Evolutionary variational-hemivariational inequalities: existence and comparison results. J. Math. Anal. Appl. 2008, 345:545-558.
    • (2008) J. Math. Anal. Appl. , vol.345 , pp. 545-558
    • Carl, S.1    Le, V.K.2    Motreanu, D.3
  • 12
    • 4844224100 scopus 로고    scopus 로고
    • A theory of discretization for nonlinear evolution inequalities applied to parabolic Signorini problems
    • Carstensen C., Gwinner J. A theory of discretization for nonlinear evolution inequalities applied to parabolic Signorini problems. Ann. Mat. Pura Appl. 1999, 177:363-394.
    • (1999) Ann. Mat. Pura Appl. , vol.177 , pp. 363-394
    • Carstensen, C.1    Gwinner, J.2
  • 16
    • 70350321978 scopus 로고    scopus 로고
    • Finite difference approximation of a parabolic hemivariational inequalities arising from temperature control problem
    • Wang Guanghui, Yang Xiaozong Finite difference approximation of a parabolic hemivariational inequalities arising from temperature control problem. Int. J. Numer. Anal. Model. 2010, 7:108-124.
    • (2010) Int. J. Numer. Anal. Model. , vol.7 , pp. 108-124
    • Wang, G.1    Yang, X.2
  • 19
    • 84855824600 scopus 로고    scopus 로고
    • Convergence of Rothe scheme for hemivariational inequalities of parabolic type, submitted for publication.
    • P. Kalita, Convergence of Rothe scheme for hemivariational inequalities of parabolic type, submitted for publication. arxiv:1108.5469.
    • Kalita, P.1
  • 21
    • 0033117219 scopus 로고    scopus 로고
    • A class of evolution hemivariational inequalities
    • Liu Z. A class of evolution hemivariational inequalities. Nonlinear Anal. 1999, 36:91-100.
    • (1999) Nonlinear Anal. , vol.36 , pp. 91-100
    • Liu, Z.1
  • 22
    • 0034262033 scopus 로고    scopus 로고
    • A class of parabolic hemivariational inequalities
    • Liu Z. A class of parabolic hemivariational inequalities. Appl. Math. Mech. 2000, 21:1045-1052.
    • (2000) Appl. Math. Mech. , vol.21 , pp. 1045-1052
    • Liu, Z.1
  • 23
    • 6344291840 scopus 로고    scopus 로고
    • Some existence theorems for evolution hemivariational inequalities
    • Liu Z. Some existence theorems for evolution hemivariational inequalities. Indian J. Pure Appl. Math. 2003, 34:1165-1176.
    • (2003) Indian J. Pure Appl. Math. , vol.34 , pp. 1165-1176
    • Liu, Z.1
  • 24
    • 13744263599 scopus 로고    scopus 로고
    • Browder-Tikhonov regularization of non-coercive evolution hemivariational inequalities
    • Liu Z. Browder-Tikhonov regularization of non-coercive evolution hemivariational inequalities. Inverse Problems 2005, 21:13-20.
    • (2005) Inverse Problems , vol.21 , pp. 13-20
    • Liu, Z.1
  • 25
    • 0000392704 scopus 로고    scopus 로고
    • A parabolic hemivariational inequality
    • Miettinen M. A parabolic hemivariational inequality. Nonlinear Anal. 1996, 26:725-734.
    • (1996) Nonlinear Anal. , vol.26 , pp. 725-734
    • Miettinen, M.1
  • 26
    • 0033102408 scopus 로고    scopus 로고
    • On parabolic hemivariational inequalities and applications
    • Miettinen M., Panagiotopoulos P.D. On parabolic hemivariational inequalities and applications. Nonlinear Anal. 1999, 35:885-915.
    • (1999) Nonlinear Anal. , vol.35 , pp. 885-915
    • Miettinen, M.1    Panagiotopoulos, P.D.2
  • 27
    • 0035301563 scopus 로고    scopus 로고
    • On existence of solutions for parabolic hemivariational inequalities
    • Migórski S. On existence of solutions for parabolic hemivariational inequalities. J. Comput. Appl. Math. 2001, 129:77-87.
    • (2001) J. Comput. Appl. Math. , vol.129 , pp. 77-87
    • Migórski, S.1
  • 28
    • 2442539203 scopus 로고    scopus 로고
    • Boundary hemivariational inequality of parabolic type
    • Migórski S., Ochal A. Boundary hemivariational inequality of parabolic type. Nonlinear Anal. 2004, 54:579-596.
    • (2004) Nonlinear Anal. , vol.54 , pp. 579-596
    • Migórski, S.1    Ochal, A.2
  • 29
    • 0004435359 scopus 로고
    • On an application of Rothe's method to nonlinear parabolic variational inequalities
    • Nagase H. On an application of Rothe's method to nonlinear parabolic variational inequalities. Funkcial. Ekvac. 1989, 32:273-299.
    • (1989) Funkcial. Ekvac. , vol.32 , pp. 273-299
    • Nagase, H.1
  • 31
    • 0034373609 scopus 로고    scopus 로고
    • A posteriori error estimates for variable time-step discretizations of nonlinear evolution equations
    • Nochetto R.H., Savaré G., Verdi C. A posteriori error estimates for variable time-step discretizations of nonlinear evolution equations. Comm. Pure Appl. Math. 2000, 53:525-589.
    • (2000) Comm. Pure Appl. Math. , vol.53 , pp. 525-589
    • Nochetto, R.H.1    Savaré, G.2    Verdi, C.3
  • 32
    • 62749121081 scopus 로고    scopus 로고
    • Regularity of parabolic hemivariational inequalities with boundary conditions
    • Park D.-G., Jeong J.-M., Park S.H. Regularity of parabolic hemivariational inequalities with boundary conditions. J. Inequal. Appl. 2009, 207873.
    • (2009) J. Inequal. Appl. , pp. 207873
    • Park, D.-G.1    Jeong, J.-M.2    Park, S.H.3
  • 33
    • 80053317847 scopus 로고    scopus 로고
    • Evolution hemivariational inequality problems with doubly nonlinear operators
    • Peng Z., Liu Z. Evolution hemivariational inequality problems with doubly nonlinear operators. J. Global Optim. 2011, 51:413-427.
    • (2011) J. Global Optim. , vol.51 , pp. 413-427
    • Peng, Z.1    Liu, Z.2
  • 34
    • 84875420018 scopus 로고
    • Numerical and theoretical treating of evolution problems by the method of discretization in time, in: Jaromír Vosmanský, Miloš Zlámal (Eds.), Equadiff 6. Proceedings of the International Conference on Differential Equations and Their Applications, J.E. Purkyně University, Department of Mathematics, Brno,
    • K. Rektorys, Numerical and theoretical treating of evolution problems by the method of discretization in time, in: Jaromír Vosmanský, Miloš Zlámal (Eds.), Equadiff 6. Proceedings of the International Conference on Differential Equations and Their Applications, J.E. Purkyně University, Department of Mathematics, Brno, 1986, pp. 71-84.
    • (1986) , pp. 71-84
    • Rektorys, K.1
  • 36
    • 0001779231 scopus 로고    scopus 로고
    • Error analysis for implicit approximations to solutions of Cauchy problems
    • Rulla J. Error analysis for implicit approximations to solutions of Cauchy problems. SIAM J. Numer. Anal. 1996, 33:68-87.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 68-87
    • Rulla, J.1
  • 37
    • 0038939215 scopus 로고
    • Approximation and regularity of evolution variational inequalities
    • Savaré G. Approximation and regularity of evolution variational inequalities. Rend. Accad. Naz. Sci. XL Mem. Mat. 1993, 111:83-111.
    • (1993) Rend. Accad. Naz. Sci. XL Mem. Mat. , vol.111 , pp. 83-111
    • Savaré, G.1
  • 38
    • 0000616291 scopus 로고    scopus 로고
    • Weak solutions and maximal regularity for abstract evolution inequalities
    • Savaré G. Weak solutions and maximal regularity for abstract evolution inequalities. Adv. Math. Sci. Appl. 1996, 6:377-418.
    • (1996) Adv. Math. Sci. Appl. , vol.6 , pp. 377-418
    • Savaré, G.1
  • 39
    • 0037338728 scopus 로고    scopus 로고
    • Semilinear parabolic problems with nonstandard boundary conditions: Error estimates
    • Slodička M. Semilinear parabolic problems with nonstandard boundary conditions: Error estimates. Numer. Methods Partial Differential Equations 2003, 19:167-191.
    • (2003) Numer. Methods Partial Differential Equations , vol.19 , pp. 167-191
    • Slodička, M.1
  • 40
    • 33749001694 scopus 로고    scopus 로고
    • The logarithmic norm. History and modern theory
    • Söderlind G. The logarithmic norm. History and modern theory. BIT Numer. Math. 2006, 46:631-652.
    • (2006) BIT Numer. Math. , vol.46 , pp. 631-652
    • Söderlind, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.