Finite increment calculus (FIC): a framework for deriving enhanced computational methods in mechanics

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.