My publications on

Journal Articles, Preprints and Technical Reports

Use the doi link to navigate to the journal, the http link to navigate to the arxiv page and the .pdf directly download the arxiv preprint.

[140]	Cheuk Hin Ho, Cas van der Oord, James P. Darby, Theo Keane, Raz L. Benson, Cristian Rebolledo Espinoza, Rutvij Kulkarni, Elina Spinu, Michail Papanikolaou, Richard Tomsett, Robert M. Forrest, Jonathan J. Bean, Gábor Csányi, and Christoph Ortner. Equivariant many-body message passing interatomic potentials for magnetic materials, 2026. [ bib \| http \| http ]
[139]	James P. Darby, Joe D. Morrow, Albert P. Bartók, Volker L. Deringer, Gábor Csányi, and Christoph Ortner. Regularity priors for the linear atomic cluster expansion. Mach. Learn.: Sci. Technol., 2026. [ bib \| DOI \| http \| http ]
[138]	Dexuan Zhou, Huajie Chen, Cheuk Hin Ho, Xin Liu, and Christoph Ortner. Stochastic reconfiguration with warm-started svd, 2025. [ bib \| http \| http ]
[137]	Cheuk Hin Ho, Christoph Ortner, and Yangshuai Wang. Flexible uncertainty calibration for machine-learned interatomic potentials, 2025. [ bib \| http \| http ]
[136]	Keerati Keeratikarn, Christoph Ortner, and Jarvist Moore Frost. Machine learning intermolecular transfer integrals with compact atomic cluster representations, 2025. [ bib \| http \| http ]
[135]	Yangshuai Wang, Drake Clark, Sambit Das, Ziyan Zhu, Daniel Massatt, Vikram Gavini, Mitchell Luskin, and Christoph Ortner. An atomic cluster expansion potential for twisted multilayer graphene. Mach. Learn.: Sci. Technol., 6:18976, 2025. [ bib \| DOI \| http \| http ]
[134]	Tina Torabi, Matthias Militzer, Michael P. Friedlander, and Christoph Ortner. Scalable data-driven basis selection for linear machine learning interatomic potentials. Mach. Learn.: Sci. Technol., 7:10769, 2026. [ bib \| DOI \| http \| http ]
[133]	Rhyan Barrett, Christoph Ortner, and Julia Westermayr. Transferable machine learning potential x-mace for excited states using integrated deepsets, 2025. [ bib \| http \| http ]
[132]	Yangshuai Wang, Gabor Csanyi, and Christoph Ortner. Many-body coarse-grained molecular dynamics with the atomic cluster expansion, 2025. [ bib \| http \| http ]
[131]	Huajie Chen, Juerong Feng, Christoph Ortner, and Jack Thomas. Nearsightedness in materials with indirect band gaps, 2025. [ bib \| http \| http ]
[130]	Tina Torabi, Timon S Gutleb, and Christoph Ortner. Fast automatically differentiable matrix functions and applications in molecular simulations. Comput. Phys. Commun., 317:109832, 2025. [ bib \| DOI \| http \| http ]
[129]	Joerg Rottler and Christoph Ortner. Analysis of local structure of mechanical and thermal rearrangements in glasses with the atomic cluster expansion. J. Phys. Chem. B, 128:11492-11499, 2024. [ bib \| DOI \| http \| http ]
[128]	Matthias Sachs, Wojciech G. Stark, Reinhard J Maurer, and Christoph Ortner. Machine learning configuration-dependent friction tensors in langevin heatbaths. Mach. Learn.: Sci. Technol., 6:6670, 2025. [ bib \| DOI \| http \| http ]
[127]	Timon S Gutleb, Rhyan Barrett, Julia Westermayr, and Christoph Ortner. Parameterizing intersecting surfaces via invariants, 2024. [ bib \| http \| http ]
[126]	Jack Thomas, William J. Baldwin, Gábor Csányi, and Christoph Ortner. Self-consistent coulomb interactions for machine learning interatomic potentials. Nonlinearity, 38:095024, 2025. [ bib \| DOI \| http \| http ]
[125]	Cheuk Hin Ho, Timon S Gutleb, and Christoph Ortner. Atomic cluster expansion without self-interaction. J. Comput. Phys., 515:113271, 2024. [ bib \| DOI \| http \| http ]
[124]	Tina Torabi, Yangshuai Wang, and Christoph Ortner. Surrogate models for vibrational entropy based on a spatial decomposition. Multiscale Model. Simul., 23:514-544, 2025. [ bib \| DOI \| http \| http ]
[123]	Ilyes Batatia, Philipp Benner, Yuan Chiang, Alin M. Elena, Dávid P. Kovács, Janosh Riebesell, Xavier R. Advincula, Mark Asta, Matthew Avaylon, William J. Baldwin, Fabian Berger, Noam Bernstein, Arghya Bhowmik, Filippo Bigi, Samuel M. Blau, Vlad Cărare, Michele Ceriotti, Sanggyu Chong, James P. Darby, Sandip De, Flaviano Della Pia, Volker L. Deringer, Rokas Elijošius, Zakariya El-Machachi, Edvin Fako, Fabio Falcioni, Andrea C. Ferrari, John L. A. Gardner, Mikołaj J. Gawkowski, Annalena Genreith-Schriever, Janine George, Rhys E. A. Goodall, Jonas Grandel, Clare P. Grey, Petr Grigorev, Shuang Han, Will Handley, Hendrik H. Heenen, Kersti Hermansson, Cheuk Hin Ho, Stephan Hofmann, Christian Holm, Jad Jaafar, Konstantin S. Jakob, Hyunwook Jung, Venkat Kapil, Aaron D. Kaplan, Nima Karimitari, James R. Kermode, Panagiotis Kourtis, Namu Kroupa, Jolla Kullgren, Matthew C. Kuner, Domantas Kuryla, Guoda Liepuoniute, Chen Lin, Johannes T. Margraf, Ioan-Bogdan Magdău, Angelos Michaelides, J. Harry Moore, Aakash A. Naik, Samuel P. Niblett, Sam Walton Norwood, Niamh O'Neill, Christoph Ortner, Kristin A. Persson, Karsten Reuter, Andrew S. Rosen, Louise A. M. Rosset, Lars L. Schaaf, Christoph Schran, Benjamin X. Shi, Eric Sivonxay, Tamás K. Stenczel, Christopher Sutton, Viktor Svahn, Thomas D. Swinburne, Jules Tilly, Cas van der Oord, Santiago Vargas, Eszter Varga-Umbrich, Tejs Vegge, Martin Vondrák, Yangshuai Wang, William C. Witt, Thomas Wolf, Fabian Zills, and Gábor Csányi. A foundation model for atomistic materials chemistry. J. Chem. Phys., 163:184110, 2026. [ bib \| DOI \| http \| http ]
[122]	Yangshuai Wang, Shashwat Patel, and Christoph Ortner. A theoretical case study of the generalisation of machine-learned potentials. Comput. Methods Appl. Mech. Engrg., 422:116831, 2024. [ bib \| DOI \| http \| http ]
[121]	Ilyes Batatia, Lars Leon Schaaf, Gabor Csanyi, Christoph Ortner, and Felix Andreas Faber. Equivariant matrix function neural networks. In The Twelfth International Conference on Learning Representations, 2024. [ bib ]
[120]	David Gontier, Jianfeng Lu, and Christoph Ortner. Thermodynamic limits of electronic systems. In Density Functional Theory: Modeling, Mathematical Analysis, Computational Methods and Applications, pages 307-331. Springer, 2023. [ bib \| DOI \| http \| http ]
[119]	William C. Witt, Cas van der Oord, Elena Gelžinyté, Teemu Järvinen, Andres Ross, James P. Darby, Cheuk Hin Ho, William J. Baldwin, Matthias Sachs, James Kermode, Noam Bernstein, Gábor Csányi, and Christoph Ortner. Acepotentials.jl: A julia implementation of the atomic cluster expansion. J. Chem. Phys., 159:164101, 2023. [ bib \| DOI \| http \| http ]
[118]	Christoph Ortner. On the atomic cluster expansion: interatomic potentials and beyond. KIM REVIEW, 1, 2023. [ bib \| DOI ]
[117]	Jose M Munoz, Ilyes Batatia, Christoph Ortner, and Francesco Romeo. Retrieval of boost invariant symbolic observables via feature importance, 2023. [ bib \| http \| http ]
[116]	Ilyes Batatia, M. Geiger, Jose Munoz, T. Smidt, L. Silberman, and Christoph Ortner. A general framework for equivariant neural networks on reductive lie groups. In Proceedings of the 37th International Conference on Neural Information Processing Systems, pages 55260-55284. Curran Associates Inc., 2024. [ bib \| DOI ]
[115]	Dexuan Zhou, Huajie Chen, Cheuk Hin Ho, and Christoph Ortner. A multilevel method for many-electron schrödinger equations based on the atomic cluster expansion. SIAM J. Sci. Comput., 46:A105-A129, 2024. [ bib \| DOI \| http \| http ]
[114]	Julian Braun, Christoph Ortner, Yangshuai Wang, and Lei Zhang. Higher order far-field boundary conditions for crystalline defects. SIAM J. Numer. Anal., 63:520-541, 2025. [ bib \| DOI \| http \| http ]
[113]	Yangshuai Wang, James R Kermode, Christoph Ortner, and Lei Zhang. A posteriori error estimate and adaptivity for qm/mm models of crystalline defects. Comput. Methods Appl. Mech. Engrg., 428:117097, 2024. [ bib \| DOI \| http \| http ]
[112]	Cas van der Oord, Matthias Sachs, Dávid Péter Kovács, Christoph Ortner, and Gábor Csányi. Hyperactive learning (hal) for data-driven interatomic potentials. npj Computational Materials, 9:168, 2023. [ bib \| DOI \| http \| http ]
[111]	Gautam Anand, S. Ghosh, Liwei Zhang, A. Anupam, C. L. Freeman, Christoph Ortner, M. Eisenbach, and James R Kermode. Exploiting machine learning in multiscale modelling of materials. J. Inst. Eng. India Ser. D, 104:867-877, 2023. [ bib \| DOI ]
[110]	J. P. Darby, Dávid Péter Kovács, Ilyes Batatia, M. A. Caro, G. L. W. Hart, Christoph Ortner, and Gábor Csányi. Tensor-reduced atomic density representations. Phys. Rev. Lett., 131:028001, 2023. [ bib \| DOI \| http \| http ]
[109]	Christoph Ortner and Yangshuai Wang. A framework for a generalisation analysis of machine-learned interatomic potentials. Multiscale Model. Simul., 21:1053-1080, 2023. [ bib \| DOI \| http \| http ]
[108]	Jose M Munoz, Ilyes Batatia, and Christoph Ortner. Boost invariant polynomials for efficient jet tagging. Mach. Learn.: Sci. Technol., 3:04LT05, 2022. [ bib \| DOI \| http \| http ]
[107]	Ralf Drautz and Christoph Ortner. Atomic cluster expansion and wave function representations, 2022. [ bib \| http \| http ]
[106]	Ilyes Batatia, David P Kovacs, Gregor Simm, Christoph Ortner, and Gabor Csanyi. Mace: Higher order equivariant message passing neural networks for fast and accurate force fields. In Advances in Neural Information Processing Systems, volume 35, pages 11423-11436, 2022. [ bib \| DOI \| http \| http ]
[105]	Anton Bochkarev, Yury Lysogorskiy, Christoph Ortner, Gábor Csányi, and Ralf Drautz. Multilayer atomic cluster expansion for semi-local interactions. Phys. Rev. Res., 4:L042019, 2022. [ bib \| DOI \| http \| http ]
[104]	Ilyes Batatia, Simon Batzner, Dávid Péter Kovács, Albert Musaelian, Gregor N. C. Simm, Ralf Drautz, Christoph Ortner, Boris Kozinsky, and Gábor Csányi. The design space of e(3)-equivariant atom-centered interatomic potentials. Nature Machine Intelligence, 7:56-67, 2025. [ bib \| DOI \| http \| http ]
[103]	Xuanyu Liu, Huajie Chen, and Christoph Ortner. Convergence of the discrete minimum energy path, 2022. [ bib \| http \| http ]
[102]	Xuanyu Liu, Huajie Chen, and Christoph Ortner. Stability of the minimum energy path. Numer. Math., 156:39-70, 2024. [ bib \| DOI \| http \| http ]
[101]	S. N. Pozdnyakov, M. J. Willatt, A. P. Bartok, Christoph Ortner, Gabor Csanyi, and Michele Ceriotti. Comment on “manifolds of quasi-constant soap and acsf fingerprints and the resulting failure to machine learn four-body interactions”. J. Chem. Phys., 157:177101, 2022. [ bib \| DOI ]
[100]	Illia Kaliuzhnyi and Christoph Ortner. Optimal evaluation of symmetry-adapted n-correlations via recursive contraction of sparse symmetric tensors. J. Numer. Math., 33:87-104, 2025. [ bib \| DOI \| http \| http ]
[99]	Liwei Zhang, Berk Onat, Geneviève Dusson, Adam McSloy, Gautam Anand, Reinhard J Maurer, Christoph Ortner, and James R Kermode. Equivariant analytical mapping of first principles hamiltonians to accurate and transferable materials models. npj Computational Materials, 8:158, 2022. [ bib \| DOI \| http \| http ]
[98]	David P Kovacs, Cas van der Oord, J. Kucera, Alice Allen, D. Cole, Christoph Ortner, and Gabor Csanyi. Linear atomic cluster expansion force fields for organic molecules: beyond rmse. J. Chem. Theory Comput., 17:7696-7711, 2021. [ bib \| DOI ]
[97]	Markus Bachmayr, Geneviève Dusson, Christoph Ortner, and Jack Thomas. Polynomial approximation of symmetric functions. Math. Comp., 93:811-839, 2024. [ bib \| DOI \| http \| http ]
[96]	Sergey N. Pozdnyakov, Liwei Zhang, Christoph Ortner, Gabor Csanyi, and Michele Ceriotti. Local invertibility and sensitivity of atomic structure-feature mappings. Open Res Europe, 1:126, 2021. [ bib \| DOI \| http \| http ]
[95]	Julian Braun, Thomas Hudson, and Christoph Ortner. Asymptotic expansion of the elastic far-field of a crystalline defect. Arch. Ration. Mech. Anal., 245:1437-1490, 2022. [ bib \| DOI \| http \| http ]
[94]	Huajie Chen, Christoph Ortner, and Yangshuai Wang. Qm/mm methods for crystalline defects. part 3: Machine-learned interatomic potentials. Multiscale Model. Simul., 20:1490-1518, 2023. [ bib \| DOI \| http \| http ]
[93]	Jack Thomas, Huajie Chen, and Christoph Ortner. Body-ordered approximations of atomic properties. Arch. Ration. Mech. Anal., 245:1-60, 2022. [ bib \| DOI \| http \| http ]
[92]	Anna Kh Balci, Christoph Ortner, and Johannes Storn. Crouzeix-raviart finite element method for non-autonomous variational problems with lavrentiev gap. Numer. Math., 151:779-805, 2022. [ bib \| DOI \| http \| http ]
[91]	Felix Musil, Andrea Grisafi, Albert P. Bartók, Christoph Ortner, Gábor Csányi, and Michele Ceriotti. Physics-inspired structural representations for molecules and materials. Chem. Rev., 121:9759-9815, 2021. [ bib \| DOI \| http \| http ]
[90]	A. E. A. Allen, Geneviève Dusson, Christoph Ortner, and Gabor Csanyi. Atomic permutationally invariant polynomials for fitting molecular force fields. Mach. Learn.: Sci. Technol., 2:025017, 2021. [ bib \| DOI ]
[89]	Yury Lysogorskiy, Cas van der Oord, Anton Bochkarev, S. Menon, M. Rinaldi, T. Hammerschmidt, M. Mrovec, A. Thompson, Gábor Csányi, Christoph Ortner, and Ralf Drautz. Performant implementation of the atomic cluster expansion (pace): Application to copper and silicon. npj Computational Materials, 7:97, 2021. [ bib \| DOI \| http \| http ]
[88]	Yangshuai Wang, Huajie Chen, M. Liao, Christoph Ortner, Hao Wang, and Lei Zhang. A posteriori error estimates for adaptive qm/mm coupling methods. SIAM J. Sci. Comput., 43:A2785-A2808, 2021. [ bib \| DOI \| http \| http ]
[87]	Berk Onat, Christoph Ortner, and James R Kermode. Sensitivity and dimensionality of atomic environment representations used for machine learning interatomic potentials. J. Chem. Phys., 153:144106, 2020. [ bib \| DOI \| http \| http ]
[86]	Christoph Ortner and Jack Thomas. Point defects in tight binding models for insulators. Math. Models Methods Appl. Sci., 30:2753-2797, 2020. [ bib \| DOI \| http \| http ]
[85]	S. N. Pozdnyakov, M. J. Willatt, A. P. Bartók, Christoph Ortner, Gábor Csányi, and Michele Ceriotti. Incompleteness of atomic structure representations. Phys. Rev. Lett., 125:166001, 2020. [ bib \| DOI \| http \| http ]
[84]	Markus Bachmayr, Gabor Csanyi, Geneviève Dusson, Ralf Drautz, Simon Etter, Cas van der Oord, and Christoph Ortner. Atomic cluster expansion: Completeness, efficiency and stability. J. Comput. Phys., 454:110946, 2022. [ bib \| DOI \| http \| http ]
[83]	Derek Olson, Christoph Ortner, Yangshuai Wang, and Lei Zhang. Elastic far-field decay from dislocations in multilattices. Multiscale Model. Simul., 21:1379-1409, 2023. [ bib \| DOI \| http \| http ]
[82]	Cas van der Oord, Geneviève Dusson, Gabor Csanyi, and Christoph Ortner. Regularised atomic body-ordered permutation-invariant polynomials for the construction of interatomic potentials. Mach. Learn.: Sci. Technol., 1:6660, 2020. [ bib \| DOI \| http \| http ]
[81]	Simon Etter, D. Massat, Mitchell Luskin, and Christoph Ortner. Modeling and computation of kubo conductivity for 2d incommensurate bilayers. Multiscale Model. Simul., 18:1525-1564, 2020. [ bib \| DOI \| http \| http ]
[80]	Huajie Chen, Christoph Ortner, and Jack Thomas. Locality of interatomic forces in tight binding models for insulators. ESAIM: Math. Model. Numer. Anal., 54:2295-2318, 2020. [ bib \| DOI \| http \| http ]
[79]	Maciej Buze, Thomas Hudson, and Christoph Ortner. Analysis of cell size effects in atomistic crack propagation. ESAIM: Math. Model. Numer. Anal., 54:1821 - 1847, 2020. [ bib \| DOI \| http \| http ]
[78]	Julian Braun and Christoph Ortner. Sharp uniform convergence rate of the supercell approximation of a crystalline defect. SIAM J. Numer. Anal., 58:279-297, 2020. [ bib \| DOI \| http \| http ]
[77]	Julian Braun, M. H. Duong, and Christoph Ortner. Thermodynamic limit of the transition rate of a crystalline defect. Arch. Ration. Mech. Anal., 238:1413-1474, 2020. [ bib \| DOI \| http \| http ]
[76]	Maciej Buze, Thomas Hudson, and Christoph Ortner. Analysis of an atomistic model for anti-plane fracture. Math. Models Methods Appl. Sci., 29:2469-2521, 2019. [ bib \| DOI \| http \| http ]
[75]	Stela Makri, Christoph Ortner, and James R Kermode. A preconditioning scheme for minimum energy path finding methods. J. Chem. Phys., 150:094109, 2019. [ bib \| DOI \| http \| http ]
[74]	Letif Mones, Christoph Ortner, and Gabor Csanyi. Preconditioners for the geometry optimisation and saddle point search of molecular systems. Scientific Reports, 8:13991, 2018. [ bib \| DOI \| http \| http ]
[73]	Julian Braun, Maciej Buze, and Christoph Ortner. The effect of crystal symmetries on the locality of screw dislocation cores. SIAM J. Math. Anal., 51:1108-1136, 2019. [ bib \| DOI \| http \| http ]
[72]	A. S. Dedner, Christoph Ortner, and Huan Wu. Coupling atomistic, elasticity and boundary element models, 2017. [ bib \| http \| http ]
[71]	Huajie Chen, Faizan Q Nazar, and Christoph Ortner. Geometry equilibration of crystalline defects in quantum and atomistic descriptions. Math. Models Methods Appl. Sci., 29:419-492, 2019. [ bib \| DOI \| http \| http ]
[70]	D. Massat, S. Carr, Mitchell Luskin, and Christoph Ortner. Incommensurate heterostructures in momentum space. Multiscale Model. Simul., 16:429-451, 2018. [ bib \| DOI \| http \| http ]
[69]	L. B. Pártay, Christoph Ortner, A. P. Bartók, C. J. Pickard, and Gábor Csányi. Polytypism in the ground state structure of the lennard-jonesium. Phys. Chem. Chem. Phys., 19:19369-19376, 2017. [ bib \| DOI \| http \| http ]
[68]	H. Alrachid, Letif Mones, and Christoph Ortner. Some remarks on preconditioning molecular dynamics. SMAI J. Comp. Math., 4:57-80, 2018. [ bib \| DOI \| http \| http ]
[67]	D. Olson, Xingjie Helen Li, Christoph Ortner, and Brian Van Koten. Force-based atomistic/continuum blending for multilattices. Numer. Math., 140:703-754, 2018. [ bib \| DOI \| http \| http ]
[66]	D. Olson and Christoph Ortner. Regularity and locality of point defects in multilattices. Appl. Math. Res. Express, 1-41, 2017. [ bib \| DOI \| http \| http ]
[65]	Daniel Massatt, Mitchell Luskin, and Christoph Ortner. Electronic density of states for incommensurate layers. Multiscale Model. Simul., 15:476-499, 2017. [ bib \| DOI \| http \| http ]
[64]	A. Levitt and Christoph Ortner. Convergence and cycling in walker-type saddle search algorithms. SIAM J. Numer. Anal., 55:2204-2227, 2017. [ bib \| DOI \| http \| http ]
[63]	Huajie Chen, Jianfeng Lu, and Christoph Ortner. Thermodynamic limit of crystal defects with finite temperature tight binding. Arch. Ration. Mech. Anal., 230:701-733, 2018. [ bib \| DOI \| http \| http ]
[62]	A. Dedner, Huan Wu, and Christoph Ortner. Analysis of patch-test consistent atomistic-to-continuum coupling with higher-order finite elements. ESAIM: Math. Model. Numer. Anal., 51:2263-2288, 2017. [ bib \| DOI \| http \| http ]
[61]	A. J. Binder, Mitchell Luskin, and Christoph Ortner. Analysis of a predictor-corrector method for computationally efficient modeling of surface effects in 1d. Multiscale Model. Simul., 15:892-919, 2017. [ bib \| DOI \| http \| http ]
[60]	Matthew Dobson, M. H. Duong, and Christoph Ortner. On assessing the accuracy of defect free energy computations. ESAIM: Math. Model. Numer. Anal., 52:1315-1352, 2018. [ bib \| DOI \| http \| http ]
[59]	David Packwood, James R Kermode, Letif Mones, Noam Bernstein, J. Woolley, N. I. M. Gould, Christoph Ortner, and Gabor Csanyi. A universal preconditioner for simulating condensed phase materials. J. Chem. Phys., 144:164109, 2016. [ bib \| DOI \| http \| http ]
[58]	Faizan Q Nazar and Christoph Ortner. Locality of the thomas-fermi-von weizsäcker equations. Arch. Ration. Mech. Anal., 224:817-870, 2017. [ bib \| DOI \| http \| http ]
[57]	Huajie Chen and Christoph Ortner. Qm/mm methods for crystalline defects. part 2: Consistent energy and force-mixing. Multiscale Model. Simul., 15:184-214, 2017. [ bib \| DOI \| http \| http ]
[56]	Huajie Chen and Christoph Ortner. Qm/mm methods for crystalline defects. part 1: Locality of the tight binding model. Multiscale Model. Simul., 14:232-264, 2016. [ bib \| DOI \| http \| http ]
[55]	N. Gould, Christoph Ortner, and David Packwood. A dimer-type saddle search algorithm with preconditioning and linesearch. Math. Comp., 85:2939-2966, 2016. [ bib \| DOI \| http \| http ]
[54]	Christoph Ortner and Lei Zhang. Atomistic/continuum blending with ghost force correction. SIAM J. Sci. Comput., 38:A346-A375, 2016. [ bib \| DOI \| http \| http ]
[53]	Xingjie Helen Li, Christoph Ortner, A. Shapeev, and Brian Van Koten. Analysis of blended atomistic/continuum hybrid methods. Numer. Math., 134:275-326, 2016. [ bib \| DOI \| http \| http ]
[52]	Thomas Hudson and Christoph Ortner. Analysis of stable screw dislocation configurations in an anti-plane lattice model. SIAM J. Math. Anal., 47:291-320, 2015. [ bib \| DOI \| http \| http ]
[51]	Christoph Ortner and Lei Zhang. Energy-based atomistic-to-continuum coupling without ghost forces. Comput. Methods Appl. Mech. Engrg., 279:29-45, 2014. [ bib \| http \| http ]
[50]	Christoph Ortner, A. Shapeev, and Lei Zhang. (in-)stability and stabilisation of qnl-type atomistic-to-continuum coupling methods. Multiscale Model. Simul., 12:1258-1293, 2014. [ bib \| http \| http ]
[49]	A. Mielke, Christoph Ortner, and Y. Sengul. An approach to nonlinear viscoleasticity via metric gradient flows. SIAM J. Math. Anal., 46:1317-1347, 2014. [ bib ]
[48]	V. Ehrlacher, Christoph Ortner, and A. V. Shapeev. Analysis of boundary conditions for crystal defect atomistic simulations. Arch. Ration. Mech. Anal., 222:1217-1268, 2016. [ bib \| DOI \| http \| http ]
[47]	Thomas Hudson and Christoph Ortner. Existence and stability of a screw dislocation under anti-plane deformation. Arch. Ration. Mech. Anal., 213:887-929, 2014. [ bib \| DOI \| http \| http ]
[46]	Xingjie Helen Li, Mitchell Luskin, Christoph Ortner, and A. Shapeev. Theory-based benchmarking of the blended force-based quasicontinuum method. Comput. Methods Appl. Mech. Engrg., 268:763-781, 2014. [ bib \| DOI \| http \| http ]
[45]	Mitchell Luskin and Christoph Ortner. Atomistic-to-continuum coupling. Acta Numerica, 22:397-508, 2013. [ bib \| DOI ]
[44]	Christoph Ortner and Hao Wang. A posteriori error control for a quasicontinuum approximation of a periodic chain. IMA J. Numer. Anal., 34:977-1001, 2014. [ bib \| DOI \| http \| http ]
[43]	Christoph Ortner and A. Shapeev. Interpolants of lattice functions for the analysis of atomistic/continuum multiscale methods, 2012. [ bib \| http \| http ]
[42]	Brian Van Koten and Christoph Ortner. Symmetries of 2-lattices and second order accuracy of the cauchy-born model. Multiscale Model. Simul., 11:615-634, 2013. [ bib \| DOI \| http \| http ]
[41]	Christoph Ortner and F. Theil. Justification of the cauchy-born approximation of elastodynamics. Arch. Ration. Mech. Anal., 207:1025-1073, 2013. [ bib \| DOI \| http \| http ]
[40]	Christoph Ortner and Endre Süli. A note on linear elliptic systems on ^d, 2012. [ bib \| http \| http ]
[39]	Mitchell Luskin and Christoph Ortner. Atomistic-to-continuum coupling. Springer Encyclopedia for Applied and Computational Mathematics, 2013. [ bib ]
[38]	Xingjie Helen Li, Mitchell Luskin, and Christoph Ortner. Positive definiteness of the blended force-based quasicontinuum method. Multiscale Model. Simul., 10:1023-1045, 2012. [ bib \| DOI \| http \| http ]
[37]	Mitchell Luskin, Christoph Ortner, and Brian Van Koten. Formulation and optimization of the energy-based blended quasicontinuum method. Comput. Methods Appl. Mech. Engrg., 253:160-168, 2013. [ bib \| DOI \| http \| http ]
[36]	Bernhard Langwallner, Christoph Ortner, and Endre Süli. Atomistic-to-continuum coupling approximation of a one-dimensional toy model for density functional theory. Multiscale Model. Simul., 11:59-91, 2013. [ bib \| DOI \| http \| http ]
[35]	K. Jayawardana, C. Mordacq, Christoph Ortner, and H. S. Park. An analysis of the boundary layer in the 1d surface cauchy-born model. ESAIM: Math. Model. Numer. Anal., 47:109-123, 2013. [ bib \| DOI ]
[34]	Christoph Ortner and Lei Zhang. Construction and sharp consistency estimates for atomistic/continuum coupling methods with general interfaces: a 2d model problem. SIAM J. Numer. Anal., 50:2940-2965, 2012. [ bib \| DOI \| http \| http ]
[33]	Christoph Ortner and A. V. Shapeev. Analysis of an energy-based atomistic/continuum coupling approximation of a vacancy in the 2d triangular lattice. Math. Comp., 82:2191-2236, 2013. [ bib \| DOI \| http \| http ]
[32]	Christoph Ortner. The role of the patch test in 2d atomistic-to-continuum coupling methods. ESAIM: Math. Model. Numer. Anal., 46:1275-1319, 2012. [ bib \| DOI ]
[31]	Brian Van Koten, Xingjie Helen Li, Mitch Luskin, and Christoph Ortner. A computational and theoretical investigation of the accuracy of quasicontinuum methods. In Numerical Analysis of Multiscale Problems, pages 67-96. Springer Lecture Notes in Computational Science and Engineering 83, 2012. [ bib \| DOI ]
[30]	Matthew Dobson, Christoph Ortner, and A. V. Shapeev. The spectrum of the force-based quasicontinuum operator for a homogeneous periodic chain. Multiscale Model. Simul., 10:744-765, 2012. [ bib \| DOI \| http \| http ]
[29]	Christoph Ortner and Hao Wang. A priori error estimates for energy-based quasicontinuum approximations of a periodic chain. Math. Models Methods Appl. Sci., 21:2491-2521, 2011. [ bib \| DOI ]
[28]	Charalambos Makridakis, Christoph Ortner, and Endre Süli. Stress-based atomistic/continuum coupling: a new variant of the quasicontinuum approximation. Int. J. Multiscale Comput. Eng., 10, 2012. [ bib ]
[27]	Mitchell Luskin and Christoph Ortner. Linear stationary iterative methods for the force-based quasicontinuum approximation. In Numerical Analysis and Multiscale Computations, pages 331-368. Springer Lect. Notes Comput. Sci. Eng. Springer 82, 2012. [ bib \| DOI \| http \| http ]
[26]	Pras Pathmanathan, Christoph Ortner, and David Kay. Existence of solutions of partially degenerate visco-elastic problems, and applications to modelling muscular contraction and cardiac electro-mechanical activity, 2012. [ bib ]
[25]	Siobhan Burke, Christoph Ortner, and Endre Suli. An adaptive finite element approximation of a generalised ambrosio-tortorelli functional. Math. Models Methods Appl. Sci., 23:1663-1697, 2013. [ bib \| DOI ]
[24]	Thomas Hudson and Christoph Ortner. On the stability of bravais lattices and their cauchy-born approximations. M2AN Math. Model. Numer. Anal., 46:81-110, 2012. [ bib \| DOI ]
[23]	Charalambos Makridakis, Christoph Ortner, and Endre Süli. A priori error analysis of two force-based atomistic/continuum models of a periodic chain. Numer. Math., 119:83-121, 2011. [ bib \| DOI ]
[22]	Christoph Ortner and Winnifried Wollner. A priori error estimates for optimal control problems with pointwise constraints on the gradient of the state. Numer. Math., 118:587-600, 2011. [ bib \| DOI ]
[21]	Matthew Dobson, Mitch Luskin, and Christoph Ortner. Iterative methods for the force-based quasicontinuum approximation: Analysis of a 1d model problem. Comput. Methods Appl. Mech. Engrg., 200:2697-2709, 2011. [ bib \| DOI ]
[20]	Christoph Ortner. Nonconforming finite-element discretization of convex variational problems. IMA J. Numer. Anal., 31:847-864, 2011. [ bib \| DOI ]
[19]	Christoph Ortner. A priori and a posteriori analysis of the quasinonlocal quasicontinuum method in 1d. Math. Comp., 80:1265-1285, 2011. [ bib \| DOI ]
[18]	Christoph Ortner and Dirk Praetorius. On the convergence of adaptive nonconforming finite element methods for a class of convex variational problems. SIAM J. Numer. Anal., 49:346-367, 2011. [ bib \| DOI ]
[17]	Soren Bartels, Rudiger Muller, and Christoph Ortner. Robust a priori and a posteriori error analysis for the approximation of allen-cahn and ginzburg-landau equations past topological changes. SIAM J. Numer. Anal., 49:110-134, 2011. [ bib \| DOI ]
[16]	Siobhan Burke, Christoph Ortner, and Endre Suli. Adaptive finite element approximation of the francfort-marigo model of brittle fracture. In Approximation and computation, volume 42, pages 297-310. Springer, 2011. [ bib \| DOI ]
[15]	C. Carstensen and Christoph Ortner. Analysis of a class of penalty methods for computing singular minimizers. Comput. Methods Appl. Math., 10:137-163, 2010. [ bib \| DOI ]
[14]	Bernhard Langwallner, Christoph Ortner, and Endre Suli. Existence and convergence results for the galerkin approximation of an electronic density functional. Math. Models Methods Appl. Sci., 20:2237-2265, 2010. [ bib \| DOI ]
[13]	Matthew Dobson, Mitchell Luskin, and Christoph Ortner. Accuracy of quasicontinuum approximations near instabilities. J. Mech. Phys. Solids, 58:1741-1757, 2010. [ bib \| DOI ]
[12]	S. Ferraz-Leite, Christoph Ortner, and Dirk Praetorius. Convergence of simple adaptive galerkin schemes based on h-h/2 error estimators. Numer. Math., 116:291-316, 2010. [ bib \| DOI ]
[11]	Siobhan Burke, Christoph Ortner, and Endre Suli. An adaptive finite element approximation of a variational model of brittle fracture. SIAM J. Numer. Anal., 48:980-1012, 2010. [ bib \| DOI ]
[10]	Christopher J. Larsen, Christoph Ortner, and Endre Suli. Existence of solutions to a regularized model of dynamic fracture. Math. Models Methods Appl. Sci., 20:1021-1048, 2010. [ bib \| DOI ]
[9]	Matthew Dobson, Mitchell Luskin, and Christoph Ortner. Stability, instability, and error of the force-based quasicontinuum approximation. Arch. Ration. Mech. Anal., 197:179-202, 2010. [ bib \| DOI ]
[8]	Matthew Dobson, Mitchell Luskin, and Christoph Ortner. Sharp stability estimates for the force-based quasicontinuum approximation of homogeneous tensile deformation. Multiscale Model. Simul., 8:782-802, 2010. [ bib \| DOI ]
[7]	Annalisa Buffa and Christoph Ortner. Compact embeddings of broken sobolev spaces and applications. IMA J. Numer. Anal., 29:827-855, 2009. [ bib \| DOI ]
[6]	Mitchell Luskin and Christoph Ortner. An analysis of node-based cluster summation rules in the quasicontinuum method. SIAM J. Numer. Anal., 47:3070-3086, 2009. [ bib \| DOI ]
[5]	Christoph Ortner. A posteriori existence in numerical computations. SIAM J. Numer. Anal., 47:2550-2577, 2009. [ bib \| DOI ]
[4]	Matteo Negri and Christoph Ortner. Quasi-static crack propagation by griffith's criterion. Math. Models Methods Appl. Sci., 18:1895-1925, 2008. [ bib \| DOI ]
[3]	Christoph Ortner and Endre Suli. Analysis of a quasicontinuum method in one dimension. M2AN Math. Model. Numer. Anal., 42:57-91, 2008. [ bib \| DOI ]
[2]	Christoph Ortner and Endre Suli. Discontinuous galerkin finite element approximation of nonlinear second-order elliptic and hyperbolic systems. SIAM J. Numer. Anal., 45:1370-1397, 2007. [ bib \| DOI ]
[1]	Christoph Ortner. Gradient flows as a selection procedure for equilibria of nonconvex energies. SIAM J. Math. Anal., 38:1214-1234, 2006. [ bib \| DOI ]

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