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      The use of negative penalty functions in solving partial differential equations

      Ilanko, Sinniah; Tucker, Alan
      DOI
       10.1002/cnm.729
      Link
       www3.interscience.wiley.com
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      Citation
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      Ilanko, S. Tucker, A. (2005). The use of negative penalty functions in solving partial differential equations. Communications in Numerical Methods in Engineering, 21(3), 99-106.
      Permanent Research Commons link: https://hdl.handle.net/10289/3208
      Abstract
      In variational and optimization problems where the field variable is represented by a series of functions that individually do not satisfy the constraints, penalty functions are often used to enforce the constraint conditions approximately. The major drawback with this approach is that the error due to any violation of the constraint is not known. In a recent publication dealing with the Rayleigh-Ritz method it was shown that, by using a combination of positive and negative penalty parameters, any error due to the violation of the constraints may be kept within any desired tolerance. This paper shows that this approach may also be used in solving partial differential equations using a Galerkin's solution to Laplace's equation subject to mixed Neumann and Dirichlet boundary conditions as an example.
      Date
      2005
      Type
      Journal Article
      Publisher
      John Wiley & Sons Ltd
      Collections
      • Science and Engineering Papers [3122]
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