  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.
