Higher-order modeling of continua by finite-element, boundary-element, meshless, and wavelet methods

This paper is an overview of the higher-order modeling schemes for the continua based on finite-element, boundary-element, meshless, and wavelet methods. The first discrete numerical method is well established, so discussions are mainly focused on the last three methods. Apart from critically discussing the main theoretical, algorithmic, and implementation characteristics of the methods, the paper expounds on the relative merits and demerits of the methods. The results of a number of smooth and nonsmooth problems are presented. Finally, the future potential of the wavelet method in discrete numerical modeling of continua is explored.