A finite element method for unstructured grid smoothing

The finite element method is applied to grid smoothing for two-dimensional planar geometry. The coordinates of the grid nodes satisfy two quasi-linear elliptic equations in the form of Laplace equations in a Riemann space. By forming a Dirichlet boundary value problem, the proposed method is applicable to both structured and unstructured grids. The Riemannian metric, acting as a driving force in the grid smoothing, is computed iteratively beginning with the metric of the unsmoothed grid. Smoothing is achieved by computing the metric tensor on the dual mesh elements, which incorporates the influence of neighbor elements. Numerical examples of this smoothing methodology, demonstrating the efficiency of the proposed approach, are presented.