Improved adaptive mesh refinement for conformal hexahedral meshes

Abstract

The h-refinement is a technique to achieve the mesh adaptation during a finite element simulation. Some elements are selected because the error is higher than a given threshold: they are split. This operation creates new elements where the size of the edges is divided by 2 in the zone of high error. To produce a conformal mesh, the connection between two zones with different levels of refinement must be examined. This paper proposes a solution in the case of meshes made of hexahedra. Depending on the type of interface, a set of patterns has been designed. In each pattern, the hexahedron is split into pyramids and tetrahedra. That specific splitting stops the propagation of the refinement and allows h-refinement in numerical simulations based on hexahedra with a conformal finite element method. At the end, an application to a crack analysis is shown.