Meshless methods and partition of unity finite elements

ABSTRACT: In this paper, meshless methods and partition of unity based finite element methods are reviewed. In meshless methods, the approximation is built without the explicit connectivity information between the nodes; moving-least squares approximants and natural neighbor-based interpolants are discussed. The enrichment of the finite element approximation through the partition of unity framework is described, and recent advances in crack modeling are summarized. Key words: natural element method, extended finite element, level set method, crack discontinuities