Augmented Lagrangian for treatment of hanging nodes in hexahedral meshes

Abstract: The surge of activity in the resolution of fine scale features in the field of earth sciences over the past decade necessitates the development of robust yet simple algorithms that can tackle the various drawbacks of in silico models developed hitherto. One such drawback is that of the restrictive computational cost of finite element method in rendering resolutions to the fine scale features, while at the same time keeping the domain being modeled sufficiently large. We propose the use of the augmented lagrangian method commonly used in the treatment of hanging nodes in contact mechanics in tackling the drawback. An interface is introduced in a typical finite element mesh across which an aggressive coarsening of the finite elements is possible. The method is based upon minimizing an augmented potential energy which factors in the constraint that exists at the hanging nodes on that interface. This allows for a significant reduction in the number of finite elements comprising the mesh with concomitant reduction in the computational expense.