Numerical Algorithms

, Volume 65, Issue 2, pp 275–291 | Cite as

Solving heat conduction problems by the Direct Meshless Local Petrov-Galerkin (DMLPG) method

  • Davoud MirzaeiEmail author
  • Robert Schaback
Original Paper


As an improvement of the Meshless Local Petrov–Galerkin (MLPG), the Direct Meshless Local Petrov–Galerkin (DMLPG) method is applied here to the numerical solution of transient heat conduction problem. The new technique is based on direct recoveries of test functionals (local weak forms) from values at nodes without any detour via classical moving least squares (MLS) shape functions. This leads to an absolutely cheaper scheme where the numerical integrations will be done over low–degree polynomials rather than complicated MLS shape functions. This eliminates the main disadvantage of MLS based methods in comparison with finite element methods (FEM), namely the costs of numerical integration.


Generalized moving least squares (GMLS) approximation Meshless methods MLPG methods DMLPG methods Heat conduction problem 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IsfahanIsfahanIran
  2. 2.Institut für Numerische und Angewandte MathematikUniversität GöttingenGöttingenGermany

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