A finite element method for three-dimensional unstructured grid smoothing

The finite element method is applied to grid smoothing in three-dimensional geometry, generalizing earlier results obtained for planar geometry. The underlying set of equations for the Cartesian components of grid coordinates, based on the notion of harmonic coordinates, has a natural variational formulation. To estimate the target metric tensor that drives the elliptic grid equations, the metric tensor components are computed on a coarse-grained grid. Numerical examples illustrating the proposed approach are presented together with results from the smoothness functional, which is used to measure the quality of the resulting grid.