Comparative analysis between the maxent and the weighted least square shape functions in a collocation meshless method

In this article the behavior of a shape function based on the maximum entropy principle (maxent) is analyzed in a meshless collocation method, compared with a traditional fixed weighted least square shape function (FWLS). The maxent shape function used in this work has certain properties that are desired in a meshless collocation method, for example the positivity, the smooth and uniform aspect for different discretizations. Further, in the boundary, the approximation not depends of the shape function of the interior nodes, this property is know as a reduction of the shape function on the boundary. To compare this type of function, it was developed examples that include the solution of eliptical second order equations in 1D and 2D. The numerical results shown a better behavior of the maxent shape function compared with the FWLS, particularly in terms of the convergence and stability of the meshless collocations method that result. (C) 2016 CIMNE (Universitat Politecnica de Catalunya). Published by Elsevier Espana, S.L.U.