GSTF Journal of Mathematics, Statistics and Operations Research (JMSOR)

, 4:5

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Coupling of Adaptive Element Free Galerkin Method with Variational Multiscale Method for Two-Dimensional Transient Heat Conduction Problem

  • Siaw-Ching LiewAffiliated withDepartment of Mathematical, Universiti Teknologi Malaysia
  • , Su-Hoe YeakAffiliated withDepartment of Mathematical Sciences, Faculty of Science, Johor Darul Ta’azim


In this paper, the coupling of adaptive element free Galerkin method (EFGM) with variational multiscale method is developed to solve two-dimensional transient heat conduction problem. The EFGM is chosen to combine with the adaptive analysis since this method only use a set of particles to generate the discrete equations instead of mesh construction as in finite element method (FEM). This property makes additional nodes can be easily inserted at the high gradient regions to improve the numerical results. The refinement criteria and refinement strategy will be clearly shown for the adaptive analysis procedure. The performance of this coupling method is first validated by solving two-dimensional large localized gradient problem with available theoretical solutions. Next, this method will also be used to solve two-dimensional transient heat conduction problem. The accuracy and efficiency of the method is demonstrated by comparing the results between conventional EFGM and the proposed method. The results obtained show that this method is able to produce higher accuracy results compared with the standard element free Galerkin method.


adaptive element free Galerkin method variational method method two-dimensional transient heat conduction problem