Crossref Citations
This article has been cited by the following publications. This list is generated based on data provided by
Crossref.
Luskin, Mitchell
and
Ortner, Christoph
2009.
An Analysis of Node-Based Cluster Summation Rules in the Quasicontinuum Method.
SIAM Journal on Numerical Analysis,
Vol. 47,
Issue. 4,
p.
3070.
Ming, Pingbing
and
Yang, Jerry Zhijian
2009.
Analysis of a One-Dimensional Nonlocal Quasi-Continuum Method.
Multiscale Modeling & Simulation,
Vol. 7,
Issue. 4,
p.
1838.
Dobson, Matthew
and
Luskin, Mitchell
2009.
An Optimal Order Error Analysis of the One-Dimensional Quasicontinuum Approximation.
SIAM Journal on Numerical Analysis,
Vol. 47,
Issue. 4,
p.
2455.
Gunzburger, Max
and
Zhang, Yanzhi
2010.
A Quadrature-Rule Type Approximation to the Quasi-Continuum Method.
Multiscale Modeling & Simulation,
Vol. 8,
Issue. 2,
p.
571.
Chamoin, Ludovic
Prudhomme, Serge
Ben Dhia, H.
and
Oden, Tinsley
2010.
Ghost forces and spurious effects in atomic‐to‐continuum coupling methods by the Arlequin approach.
International Journal for Numerical Methods in Engineering,
Vol. 83,
Issue. 8-9,
p.
1081.
Blanc, X.
Le Bris, C.
Legoll, F.
and
Patz, C.
2010.
Finite-Temperature Coarse-Graining of One-Dimensional Models: Mathematical Analysis and Computational Approaches.
Journal of Nonlinear Science,
Vol. 20,
Issue. 2,
p.
241.
Zhang, Yanzhi
and
Gunzburger, Max
2010.
Quadrature-rule type approximations to the quasicontinuum method for long-range interatomic interactions.
Computer Methods in Applied Mechanics and Engineering,
Vol. 199,
Issue. 9-12,
p.
648.
Dobson, M.
Luskin, M.
and
Ortner, C.
2010.
Accuracy of quasicontinuum approximations near instabilities.
Journal of the Mechanics and Physics of Solids,
Vol. 58,
Issue. 10,
p.
1741.
Dobson, Matthew
Luskin, Mitchell
and
Ortner, Christoph
2010.
Stability, Instability, and Error of the Force-based Quasicontinuum Approximation.
Archive for Rational Mechanics and Analysis,
Vol. 197,
Issue. 1,
p.
179.
Van Koten, Brian
and
Luskin, Mitchell
2011.
Analysis of Energy-Based Blended Quasi-Continuum Approximations.
SIAM Journal on Numerical Analysis,
Vol. 49,
Issue. 5,
p.
2182.
ORTNER, CHRISTOPH
and
WANG, HAO
2011.
A PRIORI ERROR ESTIMATES FOR ENERGY-BASED QUASICONTINUUM APPROXIMATIONS OF A PERIODIC CHAIN.
Mathematical Models and Methods in Applied Sciences,
Vol. 21,
Issue. 12,
p.
2491.
Dobson, M.
Luskin, M.
and
Ortner, C.
2011.
Iterative methods for the force-based quasicontinuum approximation: Analysis of a 1D model problem.
Computer Methods in Applied Mechanics and Engineering,
Vol. 200,
Issue. 37-40,
p.
2697.
Van Koten, Brian
Li, Xingjie Helen
Luskin, Mitchell
and
Ortner, Christoph
2012.
Numerical Analysis of Multiscale Problems.
Vol. 83,
Issue. ,
p.
67.
Ortner, Christoph
2012.
The role of the patch test in 2D atomistic-to-continuum coupling methods.
ESAIM: Mathematical Modelling and Numerical Analysis,
Vol. 46,
Issue. 6,
p.
1275.
Luskin, Mitchell
and
Ortner, Christoph
2012.
Numerical Analysis of Multiscale Computations.
Vol. 82,
Issue. ,
p.
331.
Lubineau, Gilles
Azdoud, Yan
Han, Fei
Rey, Christian
and
Askari, Abe
2012.
A morphing strategy to couple non-local to local continuum mechanics.
Journal of the Mechanics and Physics of Solids,
Vol. 60,
Issue. 6,
p.
1088.
Li, Xingjie Helen
Luskin, Mitchell
and
Ortner, Christoph
2012.
Positive Definiteness of the Blended Force-Based Quasicontinuum Method.
Multiscale Modeling & Simulation,
Vol. 10,
Issue. 3,
p.
1023.
Blanc, X.
and
Legoll, F.
2013.
A numerical strategy for coarse-graining two-dimensional atomistic models at finite temperature: The membrane case.
Computational Materials Science,
Vol. 66,
Issue. ,
p.
84.
Makridakis, C.
Mitsoudis, D.
and
Rosakis, P.
2013.
On Atomistic-to-Continuum Couplings without Ghost Forces in Three Dimensions.
Applied Mathematics Research eXpress,
Makridakis, Charalambos
and
Süli, Endre
2013.
Finite Element Analysis of Cauchy–Born Approximations to Atomistic Models.
Archive for Rational Mechanics and Analysis,
Vol. 207,
Issue. 3,
p.
813.