Numerical Algorithms

, Volume 45, Issue 1–4, pp 61–74 | Cite as

A comparison of numerical integration rules for the meshless local Petrov–Galerkin method

  • Annamaria Mazzia
  • Massimiliano Ferronato
  • Giorgio Pini
  • Giuseppe Gambolati
Original Paper


The meshless local Petrov–Galerkin (MLPG) method is a mesh-free procedure for solving partial differential equations. However, the benefit in avoiding the mesh construction and refinement is counterbalanced by the use of complicated non polynomial shape functions with subsequent difficulties, and a potentially large cost, when implementing numerical integration schemes. In this paper we describe and compare some numerical quadrature rules with the aim at preserving the MLPG solution accuracy and at the same time reducing its computational cost.


Meshless methods Meshless local Petrov–Galerkin method Numerical integration rules 


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Copyright information

© Springer Science+Business Media LLC 2007

Authors and Affiliations

  • Annamaria Mazzia
    • 1
  • Massimiliano Ferronato
    • 1
  • Giorgio Pini
    • 1
  • Giuseppe Gambolati
    • 1
  1. 1.Dipartimento di Metodi e Modelli Matematici per le Scienze ApplicateUniversità degli Studi di PadovaPadovaItaly

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