On An Object Oriented Approach To Adaptive Finite Element Techniques

This paper describes a object oriented implementation of the h-p-adaptive finite element method for one- two- and three-dimensional approximations. The adaptive algorithm is implemented within the PZ environment and includes linear, triangular, quadrilateral, cube, tetrahedral, prismatic and pyramidal elements. This large number of elements can be refined within a single program because of the object oriented nature of the approach. Rather than concentrating on the data structure which allows to implement the different elements and refinements, the behaviour necessary to implement the refinement is emphasized.Oden, J.T., Demkowicz, L.F., (1996) Applied Functional Analysis, , CRC Press, Boca Raton, New York, London, TokyoDemkowicz, L., Devloo, P.R.B., Oden, J.T., On an h-type mesh refinement strategy based on minimization of interpolation errors (1986) Computer Methods in Applied Mechanics and Engineering, 1-2, pp. 63-87Devloo, P.R.B., Pz : An object oriented environment for scientific programming (1997) Computer Methods in Applied Mechanics and Engineering, 150, pp. 133-153Devloo, P.R.B., A three-dimensional adaptive finite element strategy (1991) Computers & Structures, 38 (2), pp. 121-130Devloo, P.R.B., (1987) An H-P Adaptive Finite Element Method for Steady Compressible Flow, , PhD thesis, The University of Texas at Austin, AugustRheinboldt, W.C., Babuska, I., Error estimates for adaptive finite element computations (1978) Siam J. Numer. Anal., 15, pp. 736-754. , augustRachowicz, W., Westermann, T.A., Oden, J.T., Demkowics, L., Toward a universal hp adaptive finite element strategy - part 2, Constrained approximation and data structure (1989) Comput. Methods Appl. Mech. Engrg., 77, pp. 113-180Kreyszig, E., (1978) Introductory Functional Analysis with Applications, , John Wiley & SonsRachowicz, W., Hardy, O., Demkowics, L., Oden, J.T., Toward a universal hp adaptive finite element strategy - part1. Constrained approximation and data structure (1989) Comput. Methods Appl. Mech. Engrg., 77, pp. 79-112Sherma, A.H., Bank, R.E., An adaptive, multi-level metho for elliptic boundary value problems (1981) Computing, 26, pp. 91-105Babuska, I., Suri, M., The p and h-p versions of the finite elements approximations: Analysis of the optimal mesh sequences in one dimension (1990) Comput. Methods Appl. Mech. Engrg., 80, pp. 5-26Zienkiewics, O.C., Zhu, J.Z., A simple error estimator and adaptive procedure for a practical engineering analysis (1987) Int. J. Num. Methods Engrg., 24, pp. 337-35