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Numerical error caused by “ghost forces” in a quasicontinuum method is studied in the context of dynamic problems. The error in the discrete W1,∞ norm is analyzed for the time scale (ε) and the time scale (1) with ε being the lattice spacing.

 In this paper, a dynamic viscoelastic problem is numerically studied. The variationalproblem is written in terms of the velocity field and it leads to a parabolic linearvariational equation. A fully discrete scheme is introduced by using thefinite element method to approximate the spatial variable andan Euler scheme to discretize time derivatives. An a priori error estimatesresult is recalled, from which the linear convergence is derived under suitableregularity conditions. Then, an a posteriorierror analysis is provided, extending some preliminary resultsobtained in the study of the heat equation and quasistatic viscoelastic problems.Upper and lower error bounds are obtained. Finally, some two-dimensionalnumerical simulations are presented to show the behavior of the error estimators.

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On the Effect of Ghost Force in the Quasicontinuum Method: Dynamic Problems in One Dimension

An a posteriori error analysis for dynamic viscoelastic problems

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On the Effect of Ghost Force in the Quasicontinuum Method: Dynamic Problems in One Dimension

An a posteriori error analysis for dynamic viscoelastic problems