Point Collocation Methods for Linear Elasticity Problems

Point collocation is the oldest way to solve partial differential equations. Methods based on collocation have been studied since decades and many variations have been proposed over the years. More recently, those methods have shown a greater interest thanks to the advances in computing hardware. The collocation methods offer a great flexibility with regards to the discretization of a defined domain and the approximation of the field derivatives. This presentation will introduce the bases of the collocation methods and of the generalized finite difference method. The importance of the selection of the nodes involved in the approximation of the field derivatives will then be presented. Finally two aspects for which the method is particularly attractive will be detailed: the solution of a PDE from a given geometry with minimum discretization effort and the adaptivity of a model based on a posteriori error estimation.