The finite element method with Lagrangian multipliers. Babuška, I. Numerische Mathematik, 20(3):179–192, 1973.
doi  abstract   bibtex   
Summary The Dirichlet problem for second order differential equations is chosen as a model problem to show how the finite element method may be implemented to avoid difficulty in fulfilling essential (stable) boundary conditions. The implementation is based on the application of Lagrangian multiplier. The rate of convergence is proved.
@Article{         Babuska_1973aa,
  abstract      = {Summary The Dirichlet problem for second order differential equations is chosen as a model problem to show how the finite element method may be implemented to avoid difficulty in fulfilling essential (stable) boundary conditions. The implementation is based on the application of Lagrangian multiplier. The rate of convergence is proved.},
  author        = {Babuška, Ivo},
  doi           = {10.1007/BF01436561},
  file          = {Babuska_1973aa.pdf},
  issn          = {0029-599X},
  journal       = {Numerische Mathematik},
  keywords      = {fem,lagrange,coupling},
  langid        = {english},
  number        = {3},
  pages         = {179--192},
  title         = {The finite element method with Lagrangian multipliers},
  volume        = {20},
  year          = {1973},
  shortjournal  = {Numer. Math.}
}

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