Mathematical Aspects of Meshless Methods

The special issue of Mathematical Problems in Engineering is published to summarize the most recent developments in meshless methods and it especially focuses on new methods and their corresponding mathematical theories. In the article titled 'Particle discrete method based on manifold cover for crack propagation of jointed rock mass' by Y. Ping et al., based on the particle contact model and the concept of manifold cover, the manifold particle discrete (MPD) method is presented. In the article titled 'The error estimates of the interpolating element-free Galerkin method for two-point boundary value problems' by J. F. Wang and co-researchers, a simpler formula of the shape function of the interpolating moving least-squares (IMLS) method is obtained. In the article titled 'The improved moving least-square Ritz method for the one-dimensional sine-Gordon equation' by Q. Wei and R. Cheng, the improved moving least-square approximation is employed to obtain the shape function of the 1D displacement field.