Luskin, Mitchell and Ortner, Christoph. (2013) Atomistic-to-continuum coupling. Acta Numerica, 22 . pp. 397-508. ISSN 0962-4929

Ortner, Christoph and Theil, Florian. (2013) Justification of the Cauchy–Born approximation of elastodynamics. Archive for Rational Mechanics and Analysis, 207 (3). pp. 1025-1073. ISSN 0003-9527

Luskin, M., Ortner, Christoph and Van Koten, B.. (2013) Formulation and optimization of the energy-based blended quasicontinuum method. Computer Methods in Applied Mechanics and Engineering, Vol.253 (No.1). pp. 160-168. ISSN 0045-7825

Langwallner, B., Ortner, C. and Süli, E.. (2013) Atomistic-to-continuum coupling approximation of a one-dimensional toy model for density functional theory. Multiscale Modeling & Simulation, Volume 11 (Number 1). pp. 59-91. ISSN 1540-3459

Ortner, Christoph and Shapeev, A. V. (2012) Interpolants of lattice functions for the analysis of atomistic/continuum multiscale methods. Working Paper. ArXiv e-prints. (ArXiv e-prints.

Ortner, Christoph and Süli, Endre (2012) A note on linear elliptic systems on $\R^d$. Working Paper. ArXiv e-prints. (ArXiv e-prints.

Ortner, Christoph and Theil, F. (2012) Nonlinear elasticity from atomistic mechanics. Working Paper. ArXiv e-prints. (ArXiv e-prints.

Koten, Brian Van and Ortner, Christoph (2012) Symmetries of 2-lattices and second order accuracy of the Cauchy--Born Model. Working Paper. ArXiv e-prints. (ArXiv e-prints.

Hudson, Thomas and Ortner, Christoph. (2012) On the stability of Bravais lattices and their Cauchy–Born approximations. ESAIM: Mathematical Modelling and Numerical Analysis, Vol.46 (No.1). pp. 81-110. ISSN 0764-583X

Ortner, Christoph. (2012) The role of the patch test in 2D atomistic-to-continuum coupling methods. ESAIM: Mathematical Modelling and Numerical Analysis, Vol.46 (No.6). pp. 1275-1319. ISSN 0764-583X

Li, Xingjie Helen, Luskin, Mitchell and Ortner, Christoph (2011) Positive-definiteness of the blended force-based quasicontinuum method. Working Paper. ArXiv e-prints. (ArXiv e-prints.

Langwallner, B., Ortner, Christoph and Süli, E. (2011) Atomistic-to-continuum coupling approximation of a one-dimensional toy model for density functional theory. Working Paper. ArXiv e-prints. (ArXiv e-prints.

Jayawardana, K., Mordacq, C., Ortner, Christoph and Park, H. S. (2011) An analysis of surface relaxation in the surface cauchy-born model. Working Paper. ArXiv e-prints. (ArXiv e-prints.

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 (No.12). pp. 2491-2521. ISSN 0218-2025

Ortner, Christoph and Zhang, Lei (2011) Construction and sharp consistency estimates for atomistic/continuum coupling methods with general interfaces : a 2D model problem. Working Paper. ArXiv e-prints. (ArXiv e-prints.

Dobson, M., Luskin, M. and Ortner, Christoph. (2011) Iterative methods for the force-based quasicontinuum approximation : analysis of a 1D model problem. Computer Methods in Applied Mechanics and Engineering, Vol.200 (No.37-40). pp. 2697-2709. ISSN 0045-7825

Makridakis, Charalambos, Ortner, Christoph and Süli, Endre. (2011) A priori error analysis of two force-based atomistic/continuum models of a periodic chain. Numerische Mathematik, Vol.119 (No.1). pp. 83-121. ISSN 0029-599X

Ortner, Christoph. (2011) Nonconforming finite-element discretization of convex variational problems. IMA Journal of Numerical Analysis, Vol.31 (No.3). pp. 847-864. ISSN 0272-4979

Ortner, Christoph and Wollner, W.. (2011) A priori error estimates for optimal control problems with pointwise constraints on the gradient of the state. Numerische Mathematik, Vol.118 (No.3). pp. 587-600. ISSN 0029-599X

Luskin, Mitchell and Ortner, Christoph (2011) Linear stationary iterative methods for the force-based quasicontinuum approximation. In: Engquist, Björn and Runborg, Olof and Tsai, Yen-Hsi R., (eds.) Numerical Analysis of Multiscale Computations. Lecture notes in computational science and engineering, Vol.82 . Berlin : Heidelberg: Springer, pp. 331-368. ISBN 9783642219429

Ortner, Christoph and Praetorius, Dirk. (2011) On the convergence of adaptive nonconforming finite element methods for a class of convex variational problems. SIAM Journal on Numerical Analysis, Vol.49 (No.1). pp. 346-367. ISSN 0036-1429

Bartels, Sören, Müller, Rüdiger and Ortner, Christoph. (2011) Robust a priori and a posteriori error analysis for the approximation of Allen–Cahn and Ginzburg–Landau equations past topological changes. SIAM Journal on Numerical Analysis, Vol.49 (No.1). pp. 110-134. ISSN 0036-1429

Koten, Brian, Li, Xingjie Helen, Luskin, Mitchell and Ortner, Christoph (2011) A computational and theoretical investigation of the accuracy of quasicontinuum methods. In: Graham, Ivan G. and Hou, Thomas Y. and Lakkis, Omar and Scheichl, Robert, (eds.) Numerical Analysis of Multiscale Problems. Lecture Notes in Computational Science and Engineering, Vol.83 . Berlin : Heidelberg: Springer, pp. 67-96. ISBN 9783642220609

Ortner, Christoph. (2011) A priori and a posteriori analysis of the quasinonlocal quasicontinuum method in 1D. Mathematics of Computation, Vol.80 (No.275). pp. 1265-1285. ISSN 0025-5718

Langwallner, Bernhard, Ortner, Christoph and Süli, Endre. (2010) Existence and convergence results for the Galerkin approximation of an electronic density functional. Mathematical Models and Methods in Applied Sciences, Vol.20 (No.12). pp. 2237-2265. ISSN 0218-2025

Dobson, M., Luskin, M. and Ortner, Christoph. (2010) Accuracy of quasicontinuum approximations near instabilities. Journal of the Mechanics and Physics of Solids, Vol.58 (No.10). pp. 1741-1757. ISSN 0022-5096

Ferraz-Leite, S., Ortner, Christoph and Praetorius, D.. (2010) Convergence of simple adaptive Galerkin schemes based on h − h/2 error estimators. Numerische Mathematik, Vol.116 (No.2). pp. 291-316. ISSN 0029-599X

Larsen, Christopher J., Ortner, Christoph and Suli, Endre. (2010) Existence of solutions to a regularized model of dynamic fracture. Mathematical Models and Methods in Applied Sciences, Vol.20 (No.7). pp. 1021-1048. ISSN 0218-2025

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 (No.1). pp. 179-202. ISSN 0003-9527

Dobson, M., Ortner, Christoph and Shapeev, A. V. (2010) The spectrum of the force-based quasicontinuum operator for a homogenous periodic chain. Working Paper. ArXiv e-prints. (ArXiv e-prints.

Burke, Siobhan, Ortner, Christoph and Süli, Endre (2010) Adaptive finite element approximation of the Francfort–Marigo model of brittle fracture. In: Gautschi, Walter and Mastroianni, Giuseppe and Rassias, Themistocles M., (eds.) Approximation and Computation. Springer optimization and its applications, Vol.42 . New York: Springer, pp. 297-310. ISBN 9781441965943

Carstensen, Carsten and Ortner, Christoph. (2010) Analysis of a class of penalty methods for computing singular minimizers. Computational Methods in Applied Mathematics, Vol.10 (No.2). pp. 137-163. ISSN 1609-4840

Dobson, M., Luskin, M. and Ortner, Christoph. (2010) Sharp stability estimates for the force-based quasicontinuum approximation of homogeneous tensile deformation. Multiscale Modeling & Simulation, Vol.8 (No.3). pp. 782-802. ISSN 1540-3459

Burke, Siobhan, Ortner, Christoph and Süli, Endre (2010) An adaptive finite element approximation of a generalised ambrosio–tortorelli functional. Working Paper. Oxford: Mathematical Institute, University of Oxford. (OxMOS Preprint Series. (Unpublished)

Burke, Siobhan, Ortner, Christoph and Süli, Endre. (2010) An adaptive finite element approximation of a variational model of brittle fracture. SIAM Journal on Numerical Analysis, Vol.48 (No.3). pp. 980-1012. ISSN 0036-1429

Buffa, A. and Ortner, Christoph. (2009) Compact embeddings of broken Sobolev spaces and applications. IMA Journal of Numerical Analysis, Vol.29 (No.4). pp. 827-855. ISSN 0272-4979

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 (No.4). pp. 3070-3086. ISSN 0036-1429

Ortner, Christoph. (2009) A posteriori existence in numerical computations. SIAM Journal on Numerical Analysis, Vol.47 (No.4). pp. 2550-2577. ISSN 0036-1429

Negri, Matteo and Ortner, Christoph. (2008) Quasi-static crack propagation by Griffith's criterion. Mathematical Models and Methods in Applied Sciences, Vol.18 (No.11). pp. 1895-1925. ISSN 0218-2025

Ortner, Christoph and Süli, Endre. (2008) Analysis of a quasicontinuum method in one dimension. ESAIM: Mathematical Modelling and Numerical Analysis, Vol.42 (No.1). pp. 57-91. ISSN 0764-583X