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Section B

Some iterative algorithms for the obstacle problems

, &
Pages 2493-2502 | Received 03 Aug 2008, Accepted 28 Nov 2008, Published online: 25 May 2010

References

  • Al-Said , E. A. , Noor , M. A. , Kayn , D. and Al-Khaled , K. 2004 . Finite difference method for solving fourth-order obstacle problems . Inter. J. Computer Math. , 81 : 741 – 748 .
  • Atkinson , K. and Han , W. 2001 . Texts in Applied Mathematics, Theoretical Numerical Analysis, A Functional Analysis Framework , Vol. 39 , Berlin : Springer .
  • Bnouhachem , A. and Noor , M. A. 2008 . A new predictor–corrector method for pseudomonotone nonlinear complementarity problems . Inter. J. Computer Math. , 85 : 1023 – 1038 .
  • Chen , Z. M. and Nochetto , R. H. 2000 . Residual type a posteriori error estimates for elliptic obstacle problems . Numer. Math. , 84 : 527 – 548 .
  • Cheng , X. L. and Xue , L. 2006 . On the error estimate of finite difference method for the obstacle problem . Appl. Math. Comput. , 183 : 416 – 422 .
  • Duvaut , G. and Lions , J.-L. 1976 . Inequalities in Mechanics and Physics , Berlin : Springer-Verlag .
  • Falk , R. S. 1974 . Error estimates for the approximation of a class of variational inequalities . Math. Comput. , 28 : 963 – 971 .
  • Friedman , A. 1982 . Variational Principles and Free Boundary Problems , New York : John Wiley .
  • Glowinski , R. 1984 . Numerical Methods for Nonlinear Variational Problems , New York : Springer-Verlag .
  • Hackbusch , W. 2006 . Elliptic Differential Equations: Theory and Numerical Treatment , Beijing : Science Press .
  • Hafner , K. 1987 . Error estimates for the finite element solution of quasilinear obstacle problems . Numer. Funct. Anal. Optim. , 9 : 415 – 433 .
  • Han , W. and Reddy , B. D. 1999 . Plasticity: Mathematical Theory and Numerical Analysis , New York : Springer-Verlag .
  • Herbin , R. 2003 . A monotonic method for the numerical solution of some free boundary value problems . SIAM J. Numer. Anal. , 40 : 2292 – 2310 .
  • Huang , H. , Han , W. and Zhou , J. 1994 . The regularization method for an obstacle problem . Numer. Math. , 69 : 155 – 166 .
  • Huang , Z. Y. and Noor , M. A. 2007 . Some new unified iteration schemes with errors for nonexpansive mappings and variational inequalities . Appl. Math. Comput. , 194 : 135 – 142 .
  • Kikuchi , N. and Oden , J. T. 1988 . Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods . SIAM, Philadelphia ,
  • Kinderlehrer , D. and Stampacchia , G. 1980 . An Introduction to Variational Inequalities and Their Applications , New York : Academic Press .
  • Kornhuber , R. 1994 . Monotone multigrid methods for elliptic variational inequalities I . Numer. Math. , 69 : 167 – 184 .
  • Kornhuber , R. 1996 . Monotone multigrid methods for elliptic variational inequalities II . Numer. Math. , 72 : 481 – 499 .
  • Liu , W. , Ma , H. and Tang , T. 2001 . On mixed error estimates for elliptic obstacle problems: A posteriori error estimation and adaptive computational methods . Adv. Comput. Math. , 15 : 261 – 283 .
  • Noor , M. A. and Al-Said , E. A. 2000 . Numerical solutions of fourth order variational inequalities . Inter. J. Computer Math. , 75 : 107 – 116 .
  • Noor , M. A. and Bnouhachem , A. 2007 . On an iterative algorithm for general variational inequalities . Appl. Math. Comput. , 185 : 155 – 168 .
  • Noor , M. A. , Yao , Y. H. , Chen , R. D. and Liou , Y. C. 2007 . An iterative method for fixed point problems and variational inequalityu problems . Math. Commun. , 12 : 121 – 132 .
  • Solodov , M. V. and Svaiter , B. F. 1999 . A new projection method for variational inequality problems . SIAM J. Control Optim. , 37 : 765 – 776 .
  • Wang , L. H. 1986 . Error estimates of two nonconforming finite elements for the obstacle problem . J. Comput. Math. , 4 : 11 – 20 .
  • Wang , L. H. 2003 . On the error estimates of nonconforming finite element approximation to the obstacle problem . J. Comput. Math. , 21 : 481 – 490 .
  • Xue , L. and Cheng , X. L. 2004 . An algorithm for solving the obstacle problems . Computers Math. Appl. , 48 : 1651 – 1657 .
  • Zhang , Y. 2001 . Multilevel projection algorithm for solving obstacle problems . Computers Math. Appl. , 41 : 1505 – 1513 .

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