A geometrical approach to mesh smoothing Original Research Article

We study the problem of smoothing finite element meshes of triangles and tetrahedra, where vertices are recursively moved to improve the overall quality of the elements with respect to a given shape quality metric. We propose a geometric approach to solving the local optimization problem. Level sets of the given metric are used to characterize the set of optimal point(s). We also introduce a new mesh quality metric for tetrahedra.