Finiteelementmethodhasbeenthedominanttechniqueincomputationalmech- icsinthepastdecades, andithasmadesigni?cantcontributionstothedevelopments in engineering and science. Nevertheless, FEM is not well suited to problems h- ing severe mesh distortion owing to extremely large deformations of materials, encountering moving discontinuities such as crack propagation along arbitrary and complex paths, involving considerable meshings and remeshings in structural optimization problems, or having multidomain of in?uence in multiphenomena physical problems. It is impossible to completely overcome those...