On the use of the extended finite element method with quadtree/octree meshes

This paper describes the use of the extended finite element method in the context of quadtree/octree meshes. Particular attention is paid to the enrichment of hanging nodes that inevitably arise with these meshes. An approach for enforcing displacement continuity along hanging edges and faces is proposed and validated on various numerical examples (holes, material interfaces, and singularities) in both 2D and 3D. Copyright © 2010 John Wiley & Sons, Ltd.