19 citations · 25 across the 2 of their papers we have counts for
5 papers
(In-)Stability and Stabilisation of QNL-Type Atomistic-to-Continuum Coupling Methods
Christoph Ortner, Alexander Shapeev, Lei Zhang
We study the stability of ghost force-free energy-based atomistic-to-continuum coupling methods. In 1D we essentially complete the theory by introducing a universally stable a/c co…
A posteriori error control for a quasicontinuum approximation of a periodic chain
Christoph Ortner, Hao Wang
We consider a 1D periodic atomistic model, for which we formulate and analyze an adaptive variant of a quasicontinuum method. We establish a posteriori error estimates for the ener…
Interpolants of Lattice Functions for the Analysis of Atomistic/Continuum Multiscale Methods
C. Ortner, A. V. Shapeev
We introduce a general class of (quasi-)interpolants of functions defined on a Bravais lattice, and establish several technical results for these interpolants that are crucial ingr…
Analysis of an Energy-based Atomistic/Continuum Coupling Approximation of a Vacancy in the 2D Triangular Lattice
Christoph Ortner, Alexander V. Shapeev
We present a comprehensive a priori error analysis of a practical energy based atomistic/continuum coupling method (Shapeev, arXiv:1010.0512) in two dimensions, for finite-range pa…
Iterative Methods for the Force-based Quasicontinuum Approximation
Matthew Dobson, Mitchell Luskin, Christoph Ortner
Force-based atomistic-continuum hybrid methods are the only known pointwise consistent methods for coupling a general atomistic model to a finite element continuum model. For this…