Related Publications on Variational/Hemivariational Inequalities and their FE Solutions

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    • Books:


    1. W. Han and B.D. Reddy , Plasticity: Mathematical Theory and Numerical Analysis, Springer-Verlag, published on April 15, 1999. Interdisciplinary Applied Mathematics, Volume 9. ISBN 0-387-98704-5.
      Review of the book from Math Reviews.
    2. W. Han and M. Sofonea , Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity, American Mathematical Society and International Press, published on November 28, 2002. AMS/IP Studies in Advanced Mathematics, Volume 30. ISBN 0-8218-3192-5.
      Review of the book from Math Reviews.
    3. M. Sofonea , W. Han, and M. Shillor , Analysis and Approximation of Contact Problems with Adhesion or Damage, Chapman-Hall/CRC Press, 2006. Pure and Applied Mathematics, Volume 276. ISBN 1-58488-585-8.
    4. W. Han and X.-L. Cheng , An Introduction to Variational Inequalities: Elementary Theory, Numerical Analysis and Applications (in Chinese: 变分不等式简介:基本理论、数值分析及应用), Higher Education Press, Beijing, 2007. ISBN 978-7-04-020880-1.

    Papers:

    1. F. Feng, W. Han, and J. Huang, The virtual element method for an obstacle problem of a Kirchhoff plate, to appear in Communications in Nonlinear Science and Numerical Simulation (CNSNS).
    2. W. Han, K. Czuprynski, and F. Jing, Mixed finite element method for a hemivariational inequality of stationary Navier-Stokes equations, Journal of Scientific Computing.
    3. M. Ling and W. Han, Minimization principle in study of a Stokes hemivariational inequality, Applied Mathematics Letters, Vol. 121 (2021), article number 107401.
    4. W. Han, A revisit of elliptic variational-hemivariational inequalities, Numerical Functional Analysis and Optimization, Vol. 42 (2021), 371-395.
    5. W. Han and C. Wang, Numerical analysis of a parabolic hemivariational inequality for semipermeable media, Journal of Computational and Applied Mathematics, Vol. 389 (2021), article number 113326.
    6. S. Migorski, W. Han, and S. Zeng, A new class of hyperbolic variational-hemivariational inequalities driven by nonlinear evolution equations, European Journal of Applied Mathematics, Vol. 32 (2021), 59-88.
    7. W. Xu, Z. Huang, W. Han, W. Chen, and C. Wang, Numerical approximation of an electro-elastic frictional contact problem modeled by hemivariational inequality, Computational and Applied Mathematics, Vol. 39 (2020), No.\ 4, Paper No.\ 265, 23 pp.
    8. W. Han, Singular perturbations of variational-hemivariational inequalities, SIAM Journal on Mathematical Analysis, Vol. 52 (2020), 1549-1566.
    9. S. Wang, W. Xu, W. Han, and W. Chen, Numerical analysis of history-dependent variational-hemivariational inequalities, Science China: Mathematics, Vol. 63 (2020), 2207-2232.
    10. W. Han, M. Jureczka, and A. Ochal, Numerical studies of a hemivariational inequality for a viscoelastic contact problem with damage, Journal of Computational and Applied Mathematics, Vol. 377 (2020), 112886.
    11. D. Han, W. Han, S. Migorski, and J. Zhao, Convergence analysis of numerical solutions for optimal control of variational-hemivariational inequalities, Applied Mathematics Letters, Vol. 105 (2020), 106327.
    12. W. Han, Minimization principles for elliptic hemivariational inequalities, Nonlinear Analysis: Real World Applications, Vol. 54 (2020), 103114.
    13. F. Jing, W. Han, Y. Zhang, and W. Yan, Analysis of an a posteriori error estimator for a variational inequality governed by the Stokes equations, Journal of Computational and Applied Mathematics, Vol. 372 (2020), 112721.
    14. D. Han, W. Han, M. Jureczka, and A. Ochal, Numerical analysis of a contact problem with wear, Computers and Mathematics with Applications, Vol. 79 (2020), 2942-2951.
    15. H. Xuan, X. Cheng, W. Han, and Q. Xiao, Numerical analysis of a dynamic contact problem with history-dependent operators, Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), 569-594.
    16. F. Wang, M. Ling, W. Han, and F. Jing, Adaptive discontinuous Galerkin methods for solving anincompressible Stokes flow problem with slip boundary condition of frictional type, Journal of Computational and Applied Mathematics, Vol. 371 (2020), 112700.
    17. C. Fang and W. Han, Stability analysis and optimal control of a stationary Stokes hemivariational inequality, Evolution Equations and Control Theory, Vol. 9 (2020), 995-1008.
    18. C. Fang, K. Czuprynski, W. Han, X.L. Cheng, and X. Dai, Finite element method for a stationary Stokes hemivariational inequality with slip boundary condition, IMA Journal of Numerical Analysis, Vol. 40 (2020), 2696-2716.
    19. W. Han and M. Sofonea, Convergence of penalty based numerical methods for variational inequalities and hemivariational inequalities, Numer. Math., Vol. 142 (2019), 917--940.
    20. W. Han and M. Sofonea, Numerical analysis of hemivariational inequalities in contact mechanics, Acta Numerica, Vol. 28 (2019), 175--286.
    21. D. Han and W. Han, Numerical analysis of an evolutionary variational-hemivariational inequality with application to a dynamic contact problem, Journal of Computational and Applied Mathematics, Vol. 358 (2019), 163--178.
    22. W. Han and Y. Li, Stability analysis of stationary variational and hemivariational inequalities with applications, Nonlinear Analysis: Real World Applications, Vol. 50 (2019), 171--191.
    23. M. Barboteu, W. Han, and S. Migorski, On numerical approximation of a variational--hemivariational inequality modeling contact problems for locking, Computers and Mathematics with Applications, Vol. 77 (2019), 2894--2905.
    24. W. Xu, Z. Huang, W. Han, W. Chen, and C. Wang, Numerical analysis of history-dependent hemivariational inequalities and applications to viscoelastic contact problems with normal penetration, Computers and Mathematics with Applications, Vol. 77 (2019), 2596--2607.
    25. W. Han, S. Migorski, and M. Sofonea, On penalty method for unilateral contact problem with non-monotone contact condition, Journal of Computational and Applied Mathematics, Vol. 356 (2019), 293--301.
    26. W. Han and S. Zeng, On convergence of numerical methods for variational-hemivariational inequalities under minimal solution regularity, Applied Mathematics Letters, Vol. 93 (2019), 105--110.
    27. W. Han, Z. Huang, C. Wang, and W. Xu, Numerical analysis of elliptic hemivariational inequalities for semipermeable media, Journal of Computational Mathematics, Vol. 37 (2019), 543--560.
    28. W. Xu, Z. Huang, W. Han, W. Chen, and C. Wang, Numerical analysis of history-dependent variational-hemivariational inequalities with applications in contact mechanics, Journal of Computational and Applied Mathematics, Vol. 351 (2019), 364--377.
    29. W. Han, M. Sofonea, and D. Danan, Numerical analysis of stationary variational-hemivariational inequalities, Numer. Math., Vol. 139 (2018), 563--592.
    30. M. Sofonea, S. Migorski, and W. Han, A penalty method for history-dependent variational-hemivariational inequalities, Computers and Mathematics with Applications, Vol. 75 (2018), 2561--2573.
    31. W. Han, Numerical analysis of stationary variational-hemivariational inequalities with applications in contact mechanics, Mathematics and Mechanics of Solids, Vol. 23 (2018), 279--293, special issue on Inequality Problems in Contact Mechanics.
    32. W. Han, M. Sofonea, and M. Barboteu, Numerical analysis of elliptic hemivariational inequalities , SIAM J. Numer. Anal., Vol. 55 (2017), 640--663.
    33. M. Barboteu, K. Bartosz, and W. Han, Numerical Analysis of an Evolutionary Variational--Hemivariational Inequality with Application in Contact Mechanics, Computer Methods in Applied Mechanics and Engineering, Vol. 318 (2017), 882--897.
    34. W. Han, S. Migorski, and M. Sofonea, Analysis of a General Dynamic History-dependent Variational-Hemivariational Inequality, Nonlinear Analysis: Real World Applications, Vol. 36 (2017), 69--88.
    35. C. Fang and W. Han, Well-posedness and optimal control of a hemivariational inequality for nonstationary Stokes fluid flow, Discrete and Continuous Dynamical Systems, Series A, Vol. 36 (2016), 5369--5386.
    36. C. Fang, W. Han, S. Migorski, and M. Sofonea, A class of hemivariational inequalities for nonstationary Navier-Stokes equations, Nonlinear Analysis: Real World Applications, Vol. 31 (2016), 257--276.
    37. M. Sofonea, W. Han, and S. Migorski, Numerical analysis of history-dependent variational–hemivariational inequalities with applications to contact problems, European Journal of Applied Mathematics, Vol. 26 (2015), 427--452.
    38. M. Barboteu, K. Bartosz, W. Han, and T. Janiczko, Numerical analysis of a hyperbolic hemivariational inequality arising in dynamic contact, SIAM Journal on Numerical Analysis, Vol. 53 (2015), 527--550.
    39. W. Han, S. Migorski, and M. Sofonea, A class of variational-hemivariational inequalities with applications to elastic contact problems, SIAM Journal on Mathematical Analysis, Vol. 46 (2014), 3891--3912.
    40. K. Kazmi, M. Barboteu, W. Han, and M. Sofonea, Numerical analysis of history-dependent quasivariational inequalities with applications in contact mechanics, ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 48 (2014), 919--942.
    41. M. Barboteu, K. Kazmi, M. Sofonea, and W. Han, Analysis of a dynamic electro-elastic problem, Zeitschrift fur Angewandte Mathematik und Mechanik (ZAMM), Vol. 93 (2013), 612--632.
    42. M. Sofonea, W. Han, and M. Barboteu, Analysis of a viscoelastic contact problem with multivalued normal compliance and unilateral constraint, Computer Methods in Applied Mechanics and Engineering, Vol. 264 (2013), 12--22.
    43. M. Sofonea, K. Kazmi, M. Barboteu, and W. Han, Analysis and numerical solution of a piezoelectric frictional contact problem, Applied Mathematical Modelling, Vol. 36 (2012), 4483--4501.
    44. W. Han, M. Sofonea, and K. Kazmi, A frictionless contact problem for electro-elastic-visco-plastic materials, Computer Methods in Applied Mechanics and Engineering, Vol. 196 (2007), 3915--3926.
    45. W. Han and M. Sofonea, On a dynamic contact problem for elastic-visco-plastic materials, Applied Numerical Mathematics, Vol. 57 (2007), 498--509. DOI (digital object identifier) information: 10.1016/j.apnum.2006.07.003.
    46. W. Han, D.-Y. Hua, and L.-H. Wang, Nonconforming finite element methods for a clamped plate with elastic unilateral obstacle, special issue of Journal of Integral Equations and Applications honoring Ken Atkinson, Vol. 18 (2006), 267--284.
    47. V. Bostan and W. Han, A posteriori error analysis for a contact problem with friction, Computer Methods in Applied Mechanics and Engineering, Vol. 195 (2006), 1252--1274.
    48. M. Campo, J. Fern\'andez, W. Han, and M. Sofonea, A dynamic viscoelastic contact problem with normal compliance and damage, Finite Elements in Analysis and Design, Vol. 42 (2005), 1--24.
    49. W. Han and K. Kazmi, Internal approximation of obstacle problems, special issue of Bull. Math. Soc. Sc. Math. Roumanie, Vol. 48 (2005), No. 2, 199--210.
    50. V. Bostan, W. Han, and B.D. Reddy, A posteriori error estimation and adaptive solution of elliptic variational inequalities of the second kind, Applied Numerical Mathematics, Vol. 52 (2005), 13--38.
    51. V. Bostan and W. Han, Recovery-based error estimation and adaptive solution of elliptic variational inequalities of the second kind, Communications in Mathematical Sciences, Vol. 2 (2004), 1--18.
    52. J. Fern\'andez, W. Han, and M. Sofonea, Numerical analysis of a frictionless viscoelastic contact problem with normal compliance, special issue of Annals of University of Craiova, Vol. 30 (2003), 97--105.
    53. O. Chau, J. Fern\'andez, W. Han, and M. Sofonea, Variational and numerical analysis of a dynamic frictionless contact problem with adhesion, Journal of Computational and Applied Mathematics, Vol. 156 (2003), 127--157.
    54. X. Cheng and W. Han, Inexact Uzawa algorithms for variational inequalities of the second kind, Computer Methods in Applied Mechanics and Engineering, Vol. 192 (2003), 1451--1462.
    55. W. Han and L.H. Wang, Non-conforming finite element analysis for a plate contact problem, SIAM Journal on Numerical Analysis, Vol. 40 (2002), 1683--1697.
    56. O. Chau, J. Fern\'andez, W. Han, and M. Sofonea, A frictionless contact problem for elastic-viscoplastic materials with normal compliance and damage, Computer Methods in Applied Mechanics and Engineering, Vol. 191 (2002), 5007--5026.
    57. M. Barboteu, W. Han, and M. Sofonea, Numerical analysis of a bilateral frictional contact problem for linearly elastic materials, IMA Journal of Numerical Analysis, Vol. 22 (2002), 407--436.
    58. O. Chau, W. Han, and M. Sofonea, A dynamic frictional contact problem with normal damped response, Acta Applicandae Mathematicae, Vol. 71 (2002), 159--178.
    59. M. Barboteu, W. Han, and M. Sofonea, A frictionless contact problem for viscoelastic materials, Journal of Applied Mathematics, Vol. 2 (2002), 1--21.
    60. W. Han, L. Kuttler, M. Shillor, and M. Sofonea, Elastic beam in adhesive contact, Int. J. Solids and Structures, Vol. 39 (2002), 1145--1164.
    61. W. Han, M. Shillor, and M. Sofonea, Variational and numerical analysis of a quasistatic viscoelastic problem with normal compliance, friction and damage, J. of Comp. and Applied Math., Vol. 137 (2001), 377--398.
    62. J. Fernandez, W. Han, M. Sofonea, and J. Viano, Variational and numerical analysis of a frictionless contact problem for elastic--viscoplastic materials with internal state variable, The Quarterly Journal of Mechanics and Applied Mathematics, Vol. 54 (2001), 501--522.
    63. W. Han and M. Sofonea, Time-dependent variational inequalities for viscoelastic contact problems, J. of Comp. and Applied Math., Vol. 136 (2001), 369--387.
    64. J. Chen, W. Han, and M. Sofonea, Numerical analysis of a contact problem in rate-type viscoplasticity, Numerical Functional Analysis and Optimization, Vol. 22 (2001), 505--527.
    65. O. Chau, W. Han, and M. Sofonea, Analysis and approximation of a viscoelastic contact problem with slip dependent friction, Dynamics of Continuous, Discrete and Impulsive Systems, Vol. 8 (2001), 153--174.
    66. J. Fern\'andez, W. Han, M. Shillor, and M. Sofonea, Numerical analysis and simulations of quasistatic frictionless contact problems, International Journal of Applied Mathematics and Computer Science (Special Issue: Mathematical Theory of Networks and Systems), Vol. 11 (2001), 205--222.
    67. J. Chen, W. Han, and M. Sofonea, Numerical analysis of a class of evolution systems arising in viscoplasticity, Computational and Applied Mathematics, Vol. 19 (2000), 279--306.
    68. J. Chen, W. Han, and M. Sofonea, Numerical analysis of a quasistatic problem of sliding frictional contact with wear, Methods and Applications of Analysis, Vol. 7 (2000), 687--704.
    69. W. Han and B.D. Reddy, Convergence of approximations to the primal problem in plasticity under conditions of minimal regularity, Numerische Mathematik, Vol. 87 (2000), 283--315.
    70. J. Chen, W. Han, and M. Sofonea, Numerical analysis of a class of evolution systems with applications in viscoplasticity, SIAM Journal on Numerical Analysis, Vol. 38 (2000), 1171--1199.
    71. W. Han and M. Sofonea, Numerical analysis of a frictionless contact problem for elastic-viscoplastic materials, Computer Methods in Applied Mechanics and Engineering, Vol. 190 (2000), 179--191.
    72. O. Chau, E.H. Essoufi, W. Han and M. Sofonea, Dynamic frictionless contact problems with normal compliance, International Journal of Differential Equations and Applications, Vol. 1 (2000), 335--361.
    73. W. Han and M. Sofonea, Evolutionary variational inequalities arising in viscoelastic contact problems, SIAM Journal on Numerical Analysis, Vol. 38 (2000), 556--579.
    74. W. Han and M. Sofonea, Analysis and numerical approximation of an elastic frictional contact problem with normal compliance, Applicationes Mathematicae, Vol. 26 (1999), 415--435.
    75. W. Han and B.D. Reddy, Convergence analysis of discrete approximations of problems in hardening plasticity, Computer Methods in Applied Mechanics and Engineering, Vol. 171 (1999), 327--340.
    76. W. Han, Error analysis of numerical solutions for a cyclic plasticity problem, Computational Mechanics, Vol. 23 (1999), 33--38.
    77. J. Chen, W. Han, and H. Huang, On the Kacanov method for a quasi-Newtonian flow problem, Numerical Functional Analysis and Optimization, Vol. 19 (1998), 961--970.
    78. W. Han, S. Jensen, and B.D. Reddy, Numerical approximations of internal variable problems in plasticity: error analysis and solution algorithms, Numerical Linear Algebra with Applications (Special Issue on Plasticity), Vol. 4 (1997), 191--204.
    79. W. Han, B.D. Reddy, and G.C. Schroeder, Qualitative and numerical analysis of quasistatic problems in elastoplasticity, SIAM Journal on Numerical Analysis, Vol. 34 (1997), 143--177.
    80. W. Han and S. Jensen, The Kacanov method for a nonlinear variational inequality of the second kind arising in elastoplasticity, Chinese Annals of Mathematics, Vol. 17B (1996), 129--138.
    81. W. Han, On the numerical approximation of a frictional contact problem with normal compliance, Numerical Functional Analysis and Optimization, Vol. 17 (1996), 307--321.
    82. W. Han and B.D. Reddy, On the finite element method for mixed variational inequalities arising in elastoplasticity, SIAM Journal on Numerical Analysis, Vol. 32 (1995), 1778--1807.
    83. W. Han, Computable error estimates for linearization and numerical solution of obstacle problems, Journal of Computational and Applied Mathematics,, Vol. 55 (1994), 69--79.
    84. H. Huang, W. Han, and J. Zhou, The regularization method for an obstacle problem, Numer. Math., Vol. 69 (1994), 155--166.
    85. W. Han, Finite element analysis of a holonomic elastic-plastic problem, Numer. Math., Vol. 60 (1992), 493--508.
    86. W. Han, Quantitative error estimates for material idealization of torsion problems, Mathematical and Computer Modelling: An International Journal, Vol. 15 (1991), No. 9, 47--54.
    87. W. Han, A regularization procedure for a simplified friction problem, Mathematical and Computer Modelling: An International Journal, Vol. 15 (1991), No. 8, 65--70.