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Meshfree/Meshless methods(MLPG)

I am using Meshless Petrov-Galerkin Method(MLPG) for non-rectangular domains. There is a flexibility of using any shape for weight function and also for local quadrature  domain. Here in my case case weight function domain and local quadrature domains are same.

 I want to know that  , for non-rectangular domains,how the different shapes of weight functions (specially circular or rectangular) will affect accuracy of the result  ?

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