Smoothing by optimisation for a quadrilateral mesh with invalid elements

In this paper, a smoothing algorithm is introduced which can be applied to a mesh with invalid elements. The first step of the method is to allow thos e invalid elements to be disconnected from the remaining mesh, This means t hat the nodes on the invalid elements are all split into two, one on the in valid element, the other on the remaining mesh, The invalid element can the n be shaped to become valid. The distance between the two copies of the sam e node is called offset. In later iterative steps, the nodes will be moved into order to reduce the offset back to zero and at the same time improve t he quality of the mesh, (C) 2000 Elsevier Science B.V. All rights reserved.