INTERNATIONAL JOURNAL OF COMPUTATIONAL ENGINEERING SCIENCE
Abstract
In thiswork, the problem of increasing the convergence order of
the integral meshless method already proposed by the same authors
is addressed. Solutions are determined through equations directly
written in discrete form over a tributary region represented by the
circle with center in the generic node and radius given by the average
of the distances between the node itself and its neighbors,
thus allowing a considerable ease in writing the discrete form of
the governing equations. The proposed approach, besides avoiding
global mesh generation, adopts interpolating polynomials, which
exactly reproduce nodal values of field variables, and eliminates
some problems typically encountered when posing Dirichlet and
Neumann boundary conditions with the Finite Element Method.
Several numerical schemes adopting extended or compact computational
cells are proposed and tested for the Laplace equation, in
line with the previous papers. Results show that, when using interpolating
polynomials that satisfy also the differential operator
in some nodes, compact computational cells characterized by the
fifth-order of convergence may be constructed.
