Published in Adv. Model. and Simul. in Eng. Sci Vol. 3 (14); 2016
In this paper we present an overview of the possibilities of the ﬁnite increment calculus (FIC) approach for deriving computational methods in mechanics with improved numerical properties for stability and accuracy. The basic concepts of the FIC procedure are presented in its application to problems of advection-diﬀusion-reaction, ﬂuid mechanics and ﬂuid-structure interaction solved with the ﬁnite element method (FEM). Examples of the good features of the FIC/FEM technique for solving some of these problems are given. A brief outline of the possibilities of the FIC/FEM approach for error estimation and mesh adaptivity is given.