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A Posteriori Error Estimation and Adaptive Algorithm for Atomistic/Continuum Coupling in Two Dimensions
Hao Wang, Mingjie Liao, Ping Lin and Lei Zhang SIAM Journal on Scientific Computing 40(4) A2087 (2018) https://doi.org/10.1137/17M1131106
Analysis of the Residual-Type and the Gradient Recovery-Type a Posteriori Error Estimators for a Consistent Atomistic-to-Continuum Coupling Method in One-Dimension
Analysis of an optimization-based atomistic-to-continuum coupling method for point defects
Derek Olson, Alexander V. Shapeev, Pavel B. Bochev and Mitchell Luskin ESAIM: Mathematical Modelling and Numerical Analysis 50(1) 1 (2016) https://doi.org/10.1051/m2an/2015023
Analysis of Boundary Conditions for Crystal Defect Atomistic Simulations
Marta Lewicka and Pablo Ochoa Springer Proceedings in Mathematics & Statistics, Differential Geometry and Continuum Mechanics 137 279 (2015) https://doi.org/10.1007/978-3-319-18573-6_10
Encyclopedia of Applied and Computational Mathematics
Mitchell Luskin and Christoph Ortner Lecture Notes in Computational Science and Engineering, Numerical Analysis of Multiscale Computations 82 331 (2012) https://doi.org/10.1007/978-3-642-21943-6_14
Consistent Energy-Based Atomistic/Continuum Coupling for Two-Body Potentials in One and Two Dimensions