Christoph Ortner

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.

[114] J. Braun, C. Ortner, Y. Wang, and L. Zhang. Higher order far-field boundary conditions for crystalline defects. ArXiv e-prints, 2210.05573, 2022. [ bib | http | .pdf ]
[113] Y. Wang, J. R. Kermode, C. Ortner, and L. Zhang. A posteriori error estimate and adaptivity for qm/mm models of crystalline defects. ArXiv e-prints, 2210.04856, 2022. [ bib | http | .pdf ]
[112] C. van der Oord, M. Sachs, D. P. Kovács, C. Ortner, and Csányi. Hyperactive learning (hal) for data-driven interatomic potentials. ArXiv e-prints, 2210.04225, 2022. [ bib | http | .pdf ]
[111] G. Anand, S. Ghosh, L. Zhang, A. Anupam, C. L. Freeman, C. Ortner, M. Eisenbach, and J. R. Kermode. Exploiting machine learning in multiscale modelling of materials. J. Inst. Eng. India Ser. D, 2022. [ bib | DOI ]
[110] J. P. Darby, D. P. Kovács, I. Batatia, M. A. Caro, G. L. W. Hart, C. Ortner, and G. Csányi. Tensor-reduced atomic density representations. ArXiv e-prints, 2210.01705, 2022. [ bib | http | .pdf ]
[109] C. Ortner and Y. Wang. A framework for a generalisation analysis of machine-learned interatomic potentials. ArXiv e-prints, 2209.05366, 2022. [ bib | http | .pdf ]
[108] J. M Munoz, I. Batatia, and C. Ortner. Bip: Boost invariant polynomials for efficient jet tagging. ArXiv e-prints, 2207.08272, 2022. [ bib | http | .pdf ]
[107] R. Drautz and C. Ortner. Atomic cluster expansion and wave function representations. ArXiv e-prints, 2206.11375, 2022. [ bib | http | .pdf ]
[106] Ilyes Batatia, Dávid Péter Kovács, Gregor N. C. Simm, Christoph Ortner, and Gábor Csányi. Mace: Higher order equivariant message passing neural networks for fast and accurate force fields. ArXiv e-prints, 2206.07697, 2022. [ bib | http | .pdf ]
[105] Anton Bochkarev, Yury Lysogorskiy, Christoph Ortner, Gábor Csányi, and Ralf Drautz. Multilayer atomic cluster expansion for semi-local interactions. ArXiv e-prints, 2205.08177, 2022. [ bib | http | .pdf ]
[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. ArXiv e-prints, 2205.06643, 2022. [ bib | http | .pdf ]
[103] Xuanyu Liu, Huajie Chen, and Christoph Ortner. Convergence of the discrete minimum energy path. ArXiv e-prints, 2204.07467, 2022. [ bib | http | .pdf ]
[102] Xuanyu Liu, Huajie Chen, and Christoph Ortner. Stability of the minimum energy path. ArXiv e-prints, 2204.00984, 2022. [ bib | http | .pdf ]
[101] S. N. Pozdnyakov, M. J. Willatt, A. P. Bartok, C. Ortner, G. Csanyi, and M. 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. ArXiv e-prints, 2202.04140, 2022. [ bib | http | .pdf ]
[99] Liwei Zhang, Berk Onat, Genevieve Dusson, 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, 2022. [ bib | DOI | http | .pdf ]
[98] D. P. Kovacs, C. van der Oord, J. Kucera, A. Allen, D. Cole, C. Ortner, and G. Csanyi. Linear atomic cluster expansion force fields for organic molecules: beyond rmse. J. Chem. Theory Comput., 17, 2021. [ bib | DOI | http | .pdf ]
[97] Markus Bachmayr, Geneviève Dusson, and Christoph Ortner. Polynomial approximation of symmetric functions. ArXiv e-prints, 2109.14771, 2021. [ bib | http | .pdf ]
[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 | .pdf ]
[95] Christoph Ortner Julian Braun, Thomas Hudson. Asymptotic expansion of the elastic far-field of a crystalline defect. Arch. Ration. Mech. Anal., online, 2022. [ bib | DOI | http | .pdf ]
[94] Yangshuai Wang Huajie Chen, Christoph Ortner. Qm/mm methods for crystalline defects. part 3: Machine-learned interatomic potentials. ArXiv e-prints, 2106.14559, 2021. to appear in SIAM Multiscale Model. Simul. [ bib | http | .pdf ]
[93] Jack Thomas, Huajie Chen, and Christoph Ortner. Rigorous body-order approximations of an electronic structure potential energy landscape. ArXiv e-prints, 2106.12572, 2021. to appear in Arch. Ration. Mech. Anal. [ bib | http | .pdf ]
[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, 2022. [ bib | DOI | http | .pdf ]
[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, 2021. [ bib | DOI | http | .pdf ]
[90] A. E. A. Allen, G. Dusson, C. Ortner, and G. Csanyi. Atomic permutationally invariant polynomials for fitting molecular force fields. Mach. Learn.: Sci. Technol., 2:025017, 2021. [ bib | DOI | http | .pdf ]
[89] Y. Lysogorskiy, C. van der Oord, A. Bochkarev, S. Menon, M. Rinaldi, T. Hammerschmidt, M. Mrovec, A. Thompson, G. Csányi, C. Ortner, and R. Drautz. Performant implementation of the atomic cluster expansion (pace): Application to copper and silicon. npj Computational Materials, 7, 2021. [ bib | DOI | http | .pdf ]
[88] Y. Wang, H. Chen, M. Liao, C. Ortner, H. Wang, and L. Zhang. A posteriori error estimates for adaptive qm/mm coupling methods. SIAM J. Sci. Comput., 43, 2021. [ bib | DOI | http | .pdf ]
[87] B. Onat, C. Ortner, and James R. Kermode. Sensitivity and dimensionality of atomic environment representations used for machine learning interatomic potentials. J. Chem. Phys., 153, 2020. [ bib | DOI | http | .pdf ]
[86] C. Ortner and J. Thomas. Point defects in tight binding models for insulators. Math. Models Meth. Appl. Sc., 30(14), 2020. [ bib | DOI | http | .pdf ]
[85] S. N. Pozdnyakov, M. J. Willatt, A. P. Bartók, C. Ortner, Gábor Csányi, and Michele Ceriotti. On the completeness of atomic structure representations. Phys. Rev. Lett., 125:166001, 2020. [ bib | DOI | http | .pdf ]
[84] M. Bachmayr, G. Csanyi, G. Dusson, R. Drautz, S. Etter, C. van der Oord, and C. Ortner. Atomic cluster expansion: Completeness, efficiency and stability. J. Comp. Phys., 454, 2022. [ bib | DOI | http | .pdf ]
[83] D. Olson and C. Ortner. Theoretical study of elastic far-field decay from dislocations in multilattices. ArXiv e-prints, 1910.12269, 2019. [ bib | http | .pdf ]
[82] C. van der Oord, G. Dusson, G. Csanyi, and C. Ortner. Regularised atomic body-ordered permutation-invariant polynomials for the construction of interatomic potentials. Mach. Learn.: Sci. Technol., 1, 2020. [ bib | DOI | http | .pdf ]
[81] S. Etter, D. Massat, M. Luskin, and C. Ortner. Modeling and computation of kubo conductivity for 2d incommensurate bilayers. Multiscale Model. Simul., 18, 2020. [ bib | DOI | http | .pdf ]
[80] H. Chen, C. Ortner, and J. Thomas. Locality of interatomic forces in tight binding models for insulators. ESAIM: Math. Model. Numer. Anal., 54, 2020. [ bib | DOI | http | .pdf ]
[79] M. Buze, T. Hudson, and C. Ortner. Analysis of cell size effects in atomistic crack propagation. ESAIM: Math. Model. Numer. Anal., 54:1821 - 1847, 2020. [ bib | DOI | http | .pdf ]
[78] J. Braun and C. Ortner. Sharp uniform convergence rate of the supercell approximation of a crystalline defect. SIAM J. Numer. Anal., 58, 2020. [ bib | DOI | http | .pdf ]
[77] J. Braun, M. H. Duong, and C. Ortner. Thermodynamic limit of the transition rate of a crystalline defect. Arch. Ration. Mech. Anal., 238, 2020. [ bib | DOI | http | .pdf ]
[76] M. Buze, T. Hudson, and C. Ortner. Analysis of an atomistic model for anti-plane fracture. Math. Models Meth. Appl. Sc., 29, 2019. [ bib | DOI | http | .pdf ]
[75] S. Makri, C. Ortner, and J. R. Kermode. A preconditioning scheme for minimum energy path finding methods. J. Chem. Phys., 150, 2019. [ bib | DOI | http | .pdf ]
[74] L. Mones, C. Ortner, and G. Csanyi. Preconditioners for the geometry optimisation and saddle point search of molecular systems. Scientific Reports, 8:13991, 2018. [ bib | DOI | http | .pdf ]
[73] J. Braun, M. Buze, and C. Ortner. The effect of crystal symmetries on the locality of screw dislocation cores. SIAM J. Math. Anal., 51, 2019. [ bib | DOI | http | .pdf ]
[72] A. S. Dedner, C. Ortner, and H. Wu. Coupling atomistic, elasticity and boundary element models. ArXiv e-prints, 1709.05977, 2017. [ bib | http | .pdf ]
[71] H. Chen, F. Q. Nazar, and C. Ortner. Geometry equilibration of crystalline defects in quantum and atomistic descriptions. Math. Models Meth. Appl. Sc., 29, 2019. [ bib | DOI | http | .pdf ]
[70] D. Massat, S. Carr, M. Luskin, and C. Ortner. Incommensurate heterostructures in momentum space. SIAM Multiscale Model. Simul., 16, 2018. [ bib | DOI | http | .pdf ]
[69] L. B. Pártay, C. Ortner, A. P. Bartók, C. J. Pickard, and G. Csányi. Polytypism in the ground state structure of the lennard-jonesium. Phys. Chem. Chem. Phys., 19, 2017. [ bib | DOI | http | .pdf ]
[68] C. Ortner H. Alrachid, L. Mones. Some remarks on preconditioning molecular dynamics. SMAI J. Comp. Math., 4:57-80, 2018. [ bib | DOI | http | .pdf ]
[67] D. Olson, X. Li, C. Ortner, and B. Van Koten. Force-based atomistic/continuum blending for multilattices. Numer. Math., 140, 2018. [ bib | DOI | http | .pdf ]
[66] D. Olson and C. Ortner. Regularity and locality of point defects in multilattices. Appl. Math. Res. Express, 1-41, 2017. [ bib | DOI | http | .pdf ]
[65] D. Massatt, M. Luskin, and C. Ortner. Electronic density of states for incommensurate layers. SIAM Multiscale Model. Simul., 15, 2017. [ bib | DOI | http | .pdf ]
[64] A. Levitt and C. Ortner. Convergence and cycling in walker-type saddle search algorithms. SIAM J. Numer. Anal., 55, 2017. [ bib | DOI | http | .pdf ]
[63] H. Chen, J. Lu, and C. Ortner. Thermodynamic limit of crystal defects with finite temperature tight binding. Arch. Ration. Mech. Anal., 230, 2018. [ bib | DOI | http | .pdf ]
[62] A. Dedner, H. Wu, and C. Ortner. Analysis of patch-test consistent atomistic-to-continuum coupling with higher-order finite elements. ESAIM: Math. Model. Numer. Anal., 51, 2017. [ bib | DOI | http | .pdf ]
[61] A. J. Binder, M. Luskin, and C. Ortner. Analysis of a predictor-corrector method for computationally efficient modeling of surface effects in 1d. Multiscale Model. Simul., 15(2), 2017. [ bib | DOI | http | .pdf ]
[60] M. Dobson, M. H. Duong, and C. Ortner. On assessing the accuracy of defect free energy computations. ESAIM: Math. Model. Numer. Anal., 52, 2018. [ bib | DOI | http | .pdf ]
[59] D. Packwood, J. Kermode, L. Mones, N. Bernstein, J. Woolley, N. I. M. Gould, C. Ortner, and G. Csanyi. A universal preconditioner for simulating condensed phase materials. J. Chem. Phys., 144, 2016. [ bib | DOI | http | .pdf ]
[58] F. Q. Nazar and C. Ortner. Locality of the thomas-fermi-von weizsäcker equations. Arch. Ration. Mech. Anal., 224(3), 2017. [ bib | DOI | http | .pdf ]
[57] H. Chen and C. Ortner. QM/MM methods for crystalline defects. Part 2: Consistent energy and force-mixing. Multiscale Model. Simul., 15(1), 2017. [ bib | DOI | http | .pdf ]
[56] H. Chen and C. Ortner. QM/MM methods for crystalline defects. Part 1: Locality of the tight binding model. Multiscale Model. Simul., 14(1), 2016. [ bib | DOI | http | .pdf ]
[55] N. Gould, C. Ortner, and D. Packwood. A dimer-type saddle search algorithm with preconditioning and linesearch. Math. Comp., 85:2939-2966, 2016. [ bib | http | .pdf ]
[54] C. Ortner and L. Zhang. Atomistic/continuum blending with ghost force correction. SIAM J. Sci. Comput., 38, 2016. [ bib | DOI | http | http ]
[53] X. H. Li, C. Ortner, A. Shapeev, and B. Van Koten. Analysis of blended atomistic/continuum hybrid methods. Numer. Math., 134, 2016. [ bib | DOI | http | .pdf ]
[52] T. Hudson and C. Ortner. Analysis of stable screw dislocation configurations in an anti-plane lattice model. SIAM J. Math. Anal., 41:291-320, 2015. [ bib | http | .pdf ]
[51] C. Ortner and L. Zhang. Energy-based atomisitic-to-continuum coupling without ghost forces. Comput. Meth. Appl. Mech. Engrg., 279:29-45, 2014. [ bib | http | .pdf ]
[50] C. Ortner, A. Shapeev, and L. Zhang. (in-)stability and stabilisation of qnl-type atomistic-to-continuum coupling methods. SIAM Multiscale Model. Simul., 12:1258-1293, 2014. [ bib | http | .pdf ]
[49] A. Mielke, C. Ortner, and Y. Sengul. An approach to nonlinear viscoleasticity via metric gradient flows. SIAM J. Math. Anal., 46:1317-1347, 2014. [ bib | .pdf ]
[48] V. Ehrlacher, C. Ortner, and A. V. Shapeev. Analysis of boundary conditions for crystal defect atomistic simulations. Arch. Ration. Mech. Anal., 222, 2016. [ bib | DOI | http | .pdf ]
[47] T. Hudson and C. Ortner. Existence and stability of a screw dislocation under anti-plane deformation. Arch. Ration. Mech. Anal., 213(3):887-929, 2014. [ bib | http | .pdf ]
[46] X. Li, M. Luskin, C. Ortner, and A. Shapeev. Theory-based benchmarking of the blended force-based quasicontinuum method. Comput. Methods Appl. Mech. Engrg., 268:763-781, 2014. [ bib | http | .pdf ]
[45] M. Luskin and C. Ortner. Atomistic-to-continuum-coupling. Acta Numerica, 2013. [ bib | http | .pdf ]
[44] P. Pathmanathan, C. Ortner, and D. Kay. Existence of solutions of partially degenerate visco-elastic problems, and applications to modelling muscular contraction and cardiac electro-mechanical activity. [ bib | .pdf ]
[43] C. Ortner and H. Wang. A posteriori error control for a quasicontinuum approximation of a periodic chain. ArXiV e-prints, 1211.3346, 2012. to appear in IMA J. Numer. Anal. [ bib | .pdf ]
[42] C. Ortner and A. Shapeev. Interpolants of lattice functions for the analysis of atomistic/continuum multiscale methods. ArXiv e-prints, 1204.3705, 2012. [ bib | http | .pdf ]
[41] B. Van Koten and C. Ortner. Symmetries of 2-lattices and second order accuracy of the cauchy-born model. SIAM Multiscale Modelling and Simulation, 11, 2013. [ bib | DOI | http | .pdf ]
[40] C. Ortner and F. Theil. Justification of the cauchy-born approximation of elastodynamics. Arch. Ration. Mech. Anal., 207, 2013. [ bib | DOI | http | .pdf ]
[39] C. Ortner and E. Süli. A note on linear elliptic systems on Rd. ArXiv e-prints, 1202.3970, 2012. [ bib | http | .pdf ]
[38] M. Luskin and C. Ortner. Atomistic-to-continuum coupling. Springer Encyclopedia for Applied and Computational Mathematics, 2013. [ bib | http | .pdf ]
[37] X. Li, M. Luskin, and C. Ortner. Positive-definiteness of the blended force-based quasicontinuum method. Multiscale Model. Simul., 10, 2012. [ bib | DOI | http | .pdf ]
[36] M. Luskin, C. Ortner, and B. Van Koten. Formulation and optimization of the energy-based blended quasicontinuum method. Comput. Methods Appl. Mech. Engrg., 253, 2013. [ bib | DOI | http | .pdf ]
[35] B. Langwallner, C. Ortner, and E. Süli. Atomistic-to-Continuum Coupling Approximation of a One-Dimensional Toy Model for Density Functional Theory. Multiscale Model. Simul., 11, 2013. [ bib | DOI | http | .pdf ]
[34] K. Jayawardana, C. Mordacq, C. Ortner, and H. S. Park. An Analysis of the Boundary Layer in the 1D Surface Cauchy-Born Model. ESAIM: Math. Model. Numer. Anal., 47, 2013. [ bib | http | .pdf ]
[33] C. Ortner and L. Zhang. Construction and sharp consistency estimates for atomistic/continuum coupling methods with general interfaces: a 2D model problem. SIAM J. Numer. Anal., 50, 2012. [ bib | DOI | http | .pdf ]
[32] C. 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, 2013. [ bib | DOI | http | .pdf ]
[31] C. Ortner. The role of the patch test in 2D atomistic-to-continuum coupling methods. ESAIM Math. Model. Numer. Anal., 46, 2012. [ bib | http | .pdf ]
[30] Brian Van Koten, Xingjie Helen Li, Mitch Luskin, and Christoph Ortner. A computational and theoretical investigation of the accuracy of quasicontinuum methods. In Ivan Graham, Tom Hou, Omar Lakkis, and Rob Scheichl, editors, Numerical Analysis of Multiscale Problems. Springer Lecture Notes in Computational Science and Engineering 83, 2012. [ bib | .pdf ]
[29] M. Dobson, C. Ortner, and A. V. Shapeev. The Spectrum of the Force-Based Quasicontinuum Operator for a Homogeneous Periodic Chain. Multiscale Model. Simul., 10(3), 2012. [ bib | http | .pdf ]
[28] C. Ortner and H. Wang. A priori error estimates for energy-based quasicontinuum approximations of a periodic chain. Math. Models Methods Appl. Sc., 21:2491-2521, 2011. [ bib | DOI | http | .pdf ]
[27] C. Makridakis, C. Ortner, and E. Süli. Stress-based atomistic/continuum coupling: a new variant of the quasicontinuum approximation. Int. J. Multiscale Comp. Engrg., 10, 2012. [ bib | .pdf ]
[26] M. Luskin and C. Ortner. Linear stationary iterative methods for the force-based quasicontinuum approximation. In Bjorn Engquist, Olof Runborg, and Richard Tsai, editors, Numerical Analysis and Multiscale Computations. Springer Lect. Notes Comput. Sci. Eng. Springer 82, 2011. [ bib | http | .pdf ]
[25] Siobhan Burke, Christoph Ortner, and Endre Süli. An adaptive finite element approximation of a generalised ambrosio-tortorelli functional. Math. Models Meth. Appl. Sc., 23, 2013. [ bib | DOI | http | .pdf ]
[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 | .pdf ]
[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(1):83-121, 2011. [ bib | DOI | http | .pdf ]
[22] Christoph Ortner and Winnifried Wollner. A priori error estimates for optimal control problems with pointwise constraints on the gradient of the state. Numerische Mathematik, 118:587-600, 2011. [ bib | DOI | http | .pdf ]
[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 | http | .pdf ]
[20] Christoph Ortner. Nonconforming finite-element discretization of convex variational problems. IMA J. Numer. Anal., 31:847-864, 2011. [ bib | .pdf ]
[19] Christoph Ortner. A priori and a posteriori analysis of the quasinonlocal quasicontinuum method in 1D. Math. Comp., 80(275):1265-1285, 2011. [ bib | DOI | http | .pdf ]
[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(1):346-367, 2011. [ bib | DOI | http | .pdf ]
[17] Sören Bartels, Rüdiger Müller, 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(1):110-134, 2011. [ bib | DOI | http | .pdf ]
[16] Siobhan Burke, Christoph Ortner, and Endre Süli. Adaptive finite element approximation of the Francfort-Marigo model of brittle fracture. In Approximation and computation, volume 42 of Springer Optim. Appl., pages 297-310. Springer, New York, 2011. [ bib | .pdf ]
[15] C. Carstensen and C. Ortner. Analysis of a class of penalty methods for computing singular minimizers. Comput. Methods Appl. Math., 10(2):137-163, 2010. [ bib | .pdf ]
[14] Bernhard Langwallner, Christoph Ortner, and Endre Süli. Existence and convergence results for the Galerkin approximation of an electronic density functional. Math. Models Methods Appl. Sci., 20(12):2237-2265, 2010. [ bib | DOI | http | .pdf ]
[13] M. Dobson, M. Luskin, and C. Ortner. Accuracy of quasicontinuum approximations near instabilities. J. Mech. Phys. Solids, 58(10):1741-1757, 2010. [ bib | DOI | http | .pdf ]
[12] S. Ferraz-Leite, C. Ortner, and D. Praetorius. Convergence of simple adaptive Galerkin schemes based on h-h/2 error estimators. Numer. Math., 116(2):291-316, 2010. [ bib | DOI | http | .pdf ]
[11] Siobhan Burke, Christoph Ortner, and Endre Süli. An adaptive finite element approximation of a variational model of brittle fracture. SIAM J. Numer. Anal., 48(3):980-1012, 2010. [ bib | DOI | http | .pdf ]
[10] Christopher J. Larsen, Christoph Ortner, and Endre Süli. Existence of solutions to a regularized model of dynamic fracture. Math. Models Methods Appl. Sci., 20(7):1021-1048, 2010. [ bib | DOI | http | .pdf ]
[9] Matthew Dobson, Mitchell Luskin, and Christoph Ortner. Stability, instability, and error of the force-based quasicontinuum approximation. Arch. Ration. Mech. Anal., 197(1):179-202, 2010. [ bib | DOI | http | .pdf ]
[8] M. Dobson, M. Luskin, and C. Ortner. Sharp stability estimates for the force-based quasicontinuum approximation of homogeneous tensile deformation. Multiscale Model. Simul., 8(3):782-802, 2010. [ bib | DOI | http | .pdf ]
[7] Annalisa Buffa and Christoph Ortner. Compact embeddings of broken Sobolev spaces and applications. IMA J. Numer. Anal., 29(4):827-855, 2009. [ bib | DOI | http | .pdf ]
[6] Mitchell Luskin and Christoph Ortner. An analysis of node-based cluster summation rules in the quasicontinuum method. SIAM J. Numer. Anal., 47(4):3070-3086, 2009. [ bib | DOI | http | .pdf ]
[5] C. Ortner. A posteriori existence in numerical computations. SIAM J. Numer. Anal., 47(4):2550-2577, 2009. [ bib | DOI | http | .pdf ]
[4] Matteo Negri and Christoph Ortner. Quasi-static crack propagation by Griffith's criterion. Math. Models Methods Appl. Sci., 18(11):1895-1925, 2008. [ bib | DOI | http | .pdf ]
[3] Christoph Ortner and Endre Süli. Analysis of a quasicontinuum method in one dimension. M2AN Math. Model. Numer. Anal., 42(1):57-91, 2008. [ bib | DOI | http | .pdf ]
[2] Christoph Ortner and Endre Süli. Discontinuous Galerkin finite element approximation of nonlinear second-order elliptic and hyperbolic systems. SIAM J. Numer. Anal., 45(4):1370-1397, 2007. [ bib | DOI | http | .pdf ]
[1] Christoph Ortner. Gradient flows as a selection procedure for equilibria of nonconvex energies. SIAM J. Math. Anal., 38(4):1214-1234, 2006. [ bib | DOI | http | .pdf ]

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