An adaptive procedure based on combining finite elements with meshless methods

This paper presents a new method for combining finite elements with meshless methods, which increases the accuracy of computational solutions in a coarse mesh by adding nodes in the domain of interest. The present method shares the features of the finite element and meshless methods such as (a) the meshless interpolation of the MLS type is employed; (b) integration domains are consistent with support domains; and (c) essential boundary conditions can be applied directly. In the present method, a ground mesh with triangular or quadrilateral elements is constructed to define polygonal support domains, and then additional nodes are placed arbitrarily in a domain without the reconstruction of a mesh. The method is very useful in an adaptive calculation, because nodes can be easily added or removed without any remeshing process. This paper was recommended for publication in revised form by Associate Editor Maenghyo Cho Hyun-Gyu Kim received his B.S. degree from Seoul National University in 1990. He then received M.S. and Ph.D. degrees from KAIST in 1993 and 1998, respectively. Dr. Kim is currently a Professor at the Department of Mechanical Engineering in Seoul National University of Technology, Korea. His research interests include multi-physics coupling analysis, interfacing non-matching meshes, development of special elements, and inverse problems.