Analysis of a quasicontinuum method in one dimension

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Ortner, Christoph; Süli, Endre;

The quasicontinuum method is a coarse-graining technique for reducing the complexity of atomistic simulations in a static and quasistatic setting. In this paper we aim to give a detailed a priori and a posteriori error analysis for a quasicontinuum method in one dimensi... View more
  • References (25)
    25 references, page 1 of 3

    [1] X. Blanc, C. Le Bris and F. Legoll, Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics: the convex case. Acta Math. Appl. Sinica English Series 23 (2007) 209-216.

    [2] A. Braides and M.S. Gelli, Continuum limits of discrete systems without convexity hypotheses. Math. Mech. Solids 7 (2002) 41-66.

    [3] A. Braides, G. Dal Maso and A. Garroni, Variational formulation of softening phenomena in fracture mechanics: the onedimensional case. Arch. Ration. Mech. Anal. 146 (1999) 23-58.

    [4] A. Braides, A.J. Lew and M. Ortiz, Effective cohesive behavior of layers of interatomic planes. Arch. Ration. Mech. Anal. 180 (2006) 151-182.

    [5] F. Brezzi, J. Rappaz and P.-A. Raviart, Finite-dimensional approximation of nonlinear problems. I. Branches of nonsingular solutions. Numer. Math. 36 (1980) 1-25.

    [6] M. Dobson and M. Luskin, Analysis of a force-based quasicontinuum approximation. ESAIM: M2AN 42 (2008) 113-139.

    [7] G. Dolzmann, Optimal convergence for the finite element method in Campanato spaces. Math. Comp. 68 (1999) 1397-1427.

    [8] W. E and B. Engquist, The heterogeneous multiscale methods. Commun. Math. Sci. 1 (2003) 87-132.

    [9] W. E and P. Ming, Analysis of multiscale methods. J. Comput. Math. 22 (2004) 210-219. Special issue dedicated to the 70th birthday of Professor Zhong-Ci Shi.

    [10] W. E and P. Ming, Analysis of the local quasicontinuum method, in Frontiers and prospects of contemporary applied mathematics, Ser. Contemp. Appl. Math. CAM 6, Higher Ed. Press, Beijing (2005) 18-32.

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