000013738 001__ 13738
000013738 005__ 20161114170254.0
000013738 04107 $$aeng
000013738 046__ $$k2011-05-25
000013738 100__ $$aKuhl, D.
000013738 24500 $$aTime Adaptive Computations Using Discontinuous and Continuous Galerkin Integration Schemes

000013738 24630 $$n3.$$pComputational Methods in Structural Dynamics and Earhquake Engineering
000013738 260__ $$bNational Technical University of Athens, 2011
000013738 506__ $$arestricted
000013738 520__ $$2eng$$aThe present paper is concerned with the time adaptive numerical integration of linear and non-linear structural dynamics using p-Galerkin time integration schemes. Different versions of single and two field formulations of discontinuous as well as continuous Galerkin schemes [1,2] with arbitrary polynomial degree are compared. The order of accuracy, the numerical dissipation and the numerical effort are investigated for this generalized family of Galerkin time integration schemes. The error analyses, defining the order of accuracy, are performed by the comparison with analytically calculated solutions and numerically calculated improved solutions in linear and non-linear dynamics, respectively. It will be shown that the order of accuracy can be arbitrarily chosen by the polynomial degree of the temporal approximations, energy conservation is obtained for continuous Galerkin schemes, numerical dissipation occurs only by using discontinuous Galerkin schemes and, finally, dissipation of artificial higher frequency responses significantly reduces the time integration error in real life structural simulations. Numerically efficient Babuska-Rheinboldt type [3] error estimates as main ingredients of adaptive time integrations are proposed. By numerical simulations it can be seen that this residual based error estimate leads to results in accordance with the error compared to the analytical solution in linear dynamics and the expensive error estimate using a sup-stepping procedure in non-linear dynamics. Finally, the adaptive time stepping procedure by [4] is adapted for higher order accurate Galerkin time integration schemes. Selected examples demonstrate the properties and the performance of the proposed adaptive integration schemes. References [1] G.M. Hulbert, Time Finite Element Methods for Structural Dynamics. International Journal for Numerical Methods in Engineering, 33, 307-331, 1992. [2] M. Borri, C. Bottasso, A General Framework for Interpreting Time Finite Element Formulations. Computational Mechanics, 13, 133-142, 1993. [3] I. Babuska, C. Rheinboldt, A-Posteriori Error Estimates for the Finite Element Method. International Journal for Numerical Methods in Engineering, 12, 1597-1615, 1978. [4] O.C.Zienkiewicz, Y.M. Xie, A Simple Error and Adaptive Time Stepping Procedure for Dynamic Analysis. Earthquake Engineering and Structural Dynamics, 20, 871-887, 1991.

000013738 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000013738 653__ $$a

000013738 7112_ $$aCOMPDYN 2011 - 3rd International Thematic Conference$$cIsland of Corfu (GR)$$d2011-05-25 / 2011-05-28$$gCOMPDYN2011
000013738 720__ $$aKuhl, D.$$iGleim, T.$$iCarstens, S.
000013738 8560_ $$ffischerc@itam.cas.cz
000013738 8564_ $$s9661$$uhttps://invenio.itam.cas.cz/record/13738/files/599.pdf$$yOriginal version of the author's contribution as presented on CD, section: MS 04 Advances in Numerical Methods for Linear and Nonlinear Dynamics.
000013738 962__ $$r13401
000013738 980__ $$aPAPER