There are several mesh-free methods but in lots of literature the authors claims that EFGM is better than other mesh-free methods. So what is the criterion to compare?
Element free Galerkin method (EFGM) is one of the meshfree
method. The advantages are
EFGM was capable of analyzing structures and has a high convergence rate (more accurate) than other methods. The computational time required for EFGM is less.
EFGM has contributed most towards the analysis of fracture problems and it is easy to model when compared to other techniques. EFGM is easy to model and most of the results produced by EFG method match the desired accuracy.
As you said, based on what reasoning or criterion the authors have claimed EFGM is superior over the other mesh-free methods? In fact, it has been shown that EFGM including enhanced basis with linear elastic fracture mechanics displacement field can result in ill-conditioned moment matrix and possibly unreliable results, since the basis is not normalized. Please see the paper with the detailed discussions on the matter:
Article Fully enriched weight functions in mesh-free methods for the...
EFG is one of the most popular meshless techniques developed in last two decades. The technique is based on global weak form of governing differential equation. In general, weak form based meshless techniques are more stable and accurate than strong form based meshless methods e.g. SPH. Again the traditional EFG is not 'truly meshless' as it employs background cells/mesh for numerical integration. Many improved schemes for numerical integration and shape function construction in EFG are proposed in recent years which improves effectiveness and efficiency of the technique.
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