711 citations · 2.4k across the 77 of their papers we have counts for
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math.NA2007★ 31 cited
Goal-Oriented Adaptive Mesh Refinement for the Quasicontinuum Approximation of a Frenkel-Kontorova Model
Marcel Arndt, Mitchell Luskin
The quasicontinuum approximation is a method to reduce the atomistic degrees of freedom of a crystalline solid by piecewise linear interpolation from representative atoms that are…
math.NA2007★ 2 cited
Goal-oriented Atomistic-Continuum Adaptivity for the Quasicontinuum Approximation
Marcel Arndt, Mitchell Luskin
We give a goal-oriented a posteriori error estimator for the atomistic-continuum modeling error in the quasicontinuum method, and we use this estimator to design an adaptive algori…
math.NA2007★ 1 cited
Error Estimation and Atomistic-Continuum Adaptivity for the Quasicontinuum Approximation of a Frenkel-Kontorova Model
Marcel Arndt, Mitchell Luskin
We propose and analyze a goal-oriented a posteriori error estimator for the atomistic-continuum modeling error in the quasicontinuum method. Based on this error estimator, we devel…