A Modified Duality Method for Solving an Elasticity Problem with a Crack Extending to the Outer Boundary

  • Robert NammEmail author
  • Georgiy Tsoy
  • Ellina Vikhtenko
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 974)


A modified dual method for solving an elasticity problem with a crack extending to the outer boundary is considered. The method is based on a modified Lagrange functional. The convergence of the method is investigated in detail under a natural assumption of \(H^1\)-regularity of the solution to the crack problem. Basic duality relation for the primal and dual problems is proposed.


Non-penetration condition Crack Duality scheme Modified lagrange functional Generalized newton method 



This study was supported by the Russian Foundation for Basic Research (Project 17-01-00682 A). Numerical experiments were performed on a computational cluster of the Shared Facility Center “Data Center of FEB RAS” [20].


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Computing Center of Far Eastern Branch Russian Academy of SciencesKhabarovskRussia
  2. 2.School of Fundamental and Computer SciencesPacific National UniversityKhabarovskRussia

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