Octasection-based refinement of finite element approximations of tetrahedral meshes that guarantees shape quality

Adaptive re nement of nite element approximations on tetrahedral meshes is generally considered to be a non-trivial task. (We wish to stress that this paper deals with mesh re nement as opposed to remeshing.) The splitting of individual nite elements needs to be done with much care to prevent signi cant deterioration of the shape quality of the elements of the re ned meshes. Considerable complexity thus results, which makes it di cult to design (and even more importantly, to later maintain) adaptive tetrahedra-based simulation codes. An adaptive re nement methodology, dubbed CHARMS (conforming hierarchical adaptive re nement methods), had recently been proposed by Krysl, Grinspun, and Schr oder. The methodology streamlines and simpli es mesh re nement, since conforming (compatible) meshes always result by construction. The present work capitalizes on these conceptual developments to build a mesh re nement technique for tetrahedra. Shape quality is guaranteed for an arbitrary number of re nement levels due to our use of element octasection based on the Kuhn triangulation of the cube. Algorithms and design issues related to the inclusion of the present technique in a CHARMS-based object oriented software framework (http:==hogwarts.ucsd.edu=∼ pkrysl=CHARMS) are described