Convergence analysis of penalty based numerical methods for constrained inequality problems

  • Weimin HanEmail author
  • Mircea Sofonea


This paper presents a general convergence theory of penalty based numerical methods for elliptic constrained inequality problems, including variational inequalities, hemivariational inequalities, and variational–hemivariational inequalities. The constraint is relaxed by a penalty formulation and is re-stored as the penalty parameter tends to zero. The main theoretical result of the paper is the convergence of the penalty based numerical solutions to the solution of the constrained inequality problem as the mesh-size and the penalty parameter approach zero independently. The convergence of the penalty based numerical methods is first established for a general elliptic variational–hemivariational inequality with constraints, and then for hemivariational inequalities and variational inequalities as special cases. Applications to problems in contact mechanics are described.

Mathematics Subject Classification

65N30 65N15 74M10 74M15 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Program in Applied Mathematical and Computational Sciences (AMCS), Department of MathematicsUniversity of IowaIowa CityUSA
  2. 2.Laboratoire de Mathématiques et PhysiqueUniversité de Perpignan Via DomitiaPerpignanFrance

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