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Paper   IPM / M / 14543
School of Mathematics
  Title:   An adaptive meshless local Petrov Galerkin method based on a posteriori error estimation for the boundary layer problems
  Author(s):  M. Tatari (Joint with M. Kamranian and M. Dehghan)
  Status:   Published
  Journal: Appl. Numer. Math.
  Vol.:  111
  Year:  2017
  Pages:   181-196
  Supported by:  IPM
  Abstract:
A new adaptive moving least squares (MLS) method with variable radius of influence is presented to improve the accuracy of Meshless Local Petrov–Galerkin (MLPG) methods and to minimize the computational cost for the numerical solution of singularly perturbed boundary value problems. An error indicator based on a posteriori error estimation, accurately captures the regions of the domain with insufficient resolution and adaptively determines the new nodes location. The effectiveness of the new method is demonstrated on some singularly perturbed problems involving boundary layers.

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