The philosophy of approximation of the finite element method and its corresponding object oriented implementation is discussed. It is shown, based on examples, how the finite element method can be used to approximate most of the conservation laws. Next, it is shown how this philosophy of approximation of the finite element method is translated in an object oriented programming environment suitable for the development of finite element algorithms. Finally, recent developments of the author's research group will be presented, including a discussion of auto-adaptive techniques applied to finite element approximations.1736Bangerth, W., Using modern features of C++ for adaptive finite element methods: Dimension-independent programming in deal.II (2000) Proceedings of the 16th MACS World Congress 2000, Lausanne, Switzerland, 2000, , Michel Deville and Robert Owens, editors, Document Sessions/118-1Becker, E.B., Tinsley Oden, J., Carey, G.F., (1983) Finite Elements: An Introduction, 1. , Prentice-HallBravo, C.M.A.A., (2000) Sobre a Implementação da Técnica Hp-adaptativa Tri-dimensional Para Elementos Finitos, , PhD thesis, Faculdade de Engenharia Mecânica, UNICAMPBravo, C.M.A.A., Devloo, P.R.B., Pavanello, R., Sobre a implementação do refinamento h-p (1999) CILAMCE99 Congresso Ibero Latino Americana de Metodos Computacionais Para Engenharia, pp. 1-21. , Sao PauloDevloo, P.R.B., Oden, J.T., Pattani, P., An hp-adaptive finite element method for the numerical simulation of compressible flow (1988) Computer Methods in Applied Mechanics and Engineering, 70, pp. 203-235Devloo, P.R.B., Object oriented tools for scientific computing (2000) Engineering with Computers, 16, pp. 63-72Devloo, P.R.B., Bravo, C.M.A., An object oriented approach to adaptive finite element techniques (2000) European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS, pp. 1-21Devloo, P.R.B., Longhin, G.C., An object oriented multi-threaded multi-frontal solver (2001) XXII Iberian Latin-American Congress on Computational Methods in EngineeringDubois, P.F., (1997) Object Technology for Scientific ComputingRank, E., Krause, R., A multi-scale finite-element method (1997) Computers & Structures, (64), pp. 139-144Gurtin, M.E., (1981) An Introduction to Continuum Mechanics, , Academic PressHaney, S.W., Beating the abstraction penalty in C++ using expression templates (1996) Computers in Physics, 10 (6), pp. 552-557. , Nov/DecVeldhuizen, T.L., Rapid linear algebra in C++ (1996) Dr. Dobb's Journal, , Augus
