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

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Abstract

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.

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Authors and Affiliations

  1. Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università degli Studi di Padova, via Trieste 63, 35121, Padova, Italy

    Annamaria Mazzia, Massimiliano Ferronato, Giorgio Pini & Giuseppe Gambolati

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  1. Annamaria Mazzia
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  2. Massimiliano Ferronato
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  3. Giorgio Pini
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  4. Giuseppe Gambolati
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Correspondence to Annamaria Mazzia.

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Mazzia, A., Ferronato, M., Pini, G. et al. A comparison of numerical integration rules for the meshless local Petrov–Galerkin method. Numer Algor 45, 61–74 (2007). https://doi.org/10.1007/s11075-007-9110-6

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  • DOI: https://doi.org/10.1007/s11075-007-9110-6

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