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The surge of activity in the resolution of fine scale features in the fieldof earth sciences over the past decade necessitates the development of robustyet simple algorithms that can tackle the various drawbacks of in silico modelsdeveloped hitherto. One such drawback is that of the restrictive computationalcost of finite element method in rendering resolutions to the fine scalefeatures, while at the same time keeping the domain being modeled sufficientlylarge. We propose the use of the augmented lagrangian method commonly used inthe treatment of hanging nodes in contact mechanics in tackling the drawback.An interface is introduced in a typical finite element mesh across which anaggressive coarsening of the finite elements is possible. The method is basedupon minimizing an augmented potential energy which factors in the constraintthat exists at the hanging nodes on that interface. This allows for asignificant reduction in the number of finite elements comprising the mesh withconcomitant reduction in the computational expense.

Augmented Lagrangian for treatment of hanging nodes in hexahedral meshes