A multilevel approach for obtaining locally optimal finite element meshes

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Jimack, P.K. ; Mahmood, R. ; Walkley, M.A. ; Berzins, M. (2002)
  • Publisher: Elsevier Ltd.

In this paper we consider the adaptive finite element solution of a general class of variational problems using a combination of node insertion, node movement and edge swapping. The adaptive strategy that is proposed is based upon the construction of a hierarchy of locally optimal meshes starting with a coarse grid for which the location and connectivity of the nodes is optimized.\ud \ud This grid is then locally refined and the new mesh is optimized in the same manner. Results presented indicate that this approach is able to produce better meshes than those possible by more conventional adaptive strategies and in a relatively efficient manner.
  • References (15)
    15 references, page 1 of 2

    [1] I. Babuska, B.A. Szabo and I.N. Katz, The p-Version of the Finite Element Method, SIAM Journal on Numerical Analysis, vol.18, pp.515-545, 1981.

    [2] J.M. Ball, P.K. Jimack and T. Qi, Elastostatics in the presence of a temperature distribution or inhomogeneity, Zeitschrift Fur Angewandte Mathematic Und Physik, vol.43, pp.943-973, 1992.

    [3] R.E. Bank, PLTMG Users' Guide 7.0, SIAM, Philadelphia, 1994.

    [4] E. Ba¨nsch, An adaptive finite element strategy for the 3-dimensional time-dependent Navier-Stokes equations, Journal of Computational and Applied Mathematics, vol.36, pp.3-28, 1991.

    [5] M. Delfour, G. Payre and J.-P. Zole´sio, An optimal triangulation for second-order elliptic problems, Computer Methods in Applied Mechanics and Engineering, vol.50, pp.231-261, 1985.

    [6] L.A. Freitag and C. Ollivier Gooch, Tetrahedral mesh improvement using swapping and smoothing, International Journal for Numerical Methods in Engineering, vol.40, pp.3979-4002, 1997.

    [7] P.K. Jimack, A best approximation property of the moving finite element method, SIAM Journal on Numerical Analysis, vol.33, pp.2206-2232, 1996.

    [8] P.K. Jimack, An optimal finite element mesh for elastostatic structural analysis problems, Computers and Structures, vol.64, pp.197-208, 1997.

    [9] C. Johnson, Numerical solution of partial differential equations by the finite element method, Cambridge University Press, Cambridge, 1987.

    [10] R. Lohner, An adaptive finite element scheme for transient problems in CFD, Computer Methods in Applied Mechanics and Engineering, vol.61, pp.267-281, 1987.

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