Performance of spatial derivatives using interpolation with radial basis functions

Initially applied in the context of the Boundary Element Method as an auxiliary tool, interpolating the domain core and allowing its transformation into boundary integrals, the radial basis functions have expanded their field of application. They are currently widely used as a solution technique for partial differential equations, generating the meshless formulations of the Finite Element Method. These functions also have recently become an important numerical resource as a more straightforward solver for spatial derivatives calculation. Of course, precision is lost compared to the performance as a direct interpolation tool. Still, even so, it can be advantageous because of the complexity of procedures related to the analytical derivation of primary variables and other more classical techniques. This work evaluates a series of characteristics of the derivation procedure, such as the influence of the dimensions of the problem on the results. In this work, the initial results for the research are performed through the cubic radial function, following the guidelines of the previous works. This function has no arbitrary parameter in its structures, which is a great advantage.