If there are two coulpled diffrential equations , say f1(u,e) anf f2(u,e) ?

Now i can solve these either by weak form or minimizing least square form .

Is it possible to solve f1 by least-square and f2 by weak form ? 

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  ?