Consistent pseudo-derivatives in meshless methods Original Research Article

A meshless Petrov-Galerkin formulation is developed in which derivatives of the trial functions are obtained as a linear combination of derivatives of Shepard functions. A key contribution is the development of conditions on test functions and trial functions for nonintegrable pseudo-derivatives for Petrov-Galerkin method which pass the patch test. Numerical results show that the resulting method is substantially more accurate than the Galerkin method with Shepard approximants and exceeds the rate of convergence of linear finite elements.