Under very weak conditions any well–posed linear problem of Applied Analysis can be solved by certain meshless kernel methods to any prescribed accuracy.

Since meshless methods have been introduced to alleviate the difficulties arising in conventional finite element method, many papers on applications of meshless methods to boundary element method have been published. However, most of these papers use moving least squares approximation functions that have difficulties in prescribing essential boundary conditions. Recently, in order to strengthen...

We present a meshfree generalized finite difference method for solving Poisson's equation with diffusion coefficient that contains jump discontinuities up to several orders of magnitude. To discretize the operator, we formulate strong form uses smearing discontinuity; and conservative formulation based on locally computed Voronoi cells. Additionally, propose novel enforcing Neumann boundary con...

The MLPG method is the general basis for several variations of meshless methods presented in recent literature. The interrelation of the various meshless approaches is presented in this paper. Several variations of the meshless interpolation schemes are reviewed also. Recent developments and applications of the MLPG methods are surveyed.