2014

Ortner, Christoph and Zhang, L.. (2014) Energy-based atomistic-to-continuum coupling without ghost forces. Computer Methods in Applied Mechanics and Engineering, Volume 279 . pp. 29-45. ISSN 0045-7825

Hudson, Thomas and Ortner, Christoph. (2014) Existence and stability of a screw dislocation under anti-plane deformation. Archive for Rational Mechanics and Analysis . ISSN 0003-9527 (In Press)

Ortner, Christoph, Shapeev, A. V. and Zhang, L.. (2014) (In-)stability and stabilisation of QNL-type atomistic-to-continuum coupling methods. Multiscale Modeling & Simulation: a SIAM Interdisciplinary Journal . ISSN 1540-3459 (Submitted)

Li, Xingjie Helen, Luskin, Mitchell Barry, 1951-, Ortner, Christoph and Shapeev, A. V. . (2014) Theory-based benchmarking of the blended force-based quasicontinuum method. Computer Methods in Applied Mechanics and Engineering, Volume 268 . pp. 763-781. ISSN 0045-7825

Mielke, Alexander, 1958-, Ortner, Christoph and Şengül, Yasemin. (2014) An approach to nonlinear viscoelasticity via metric gradient flows. SIAM Journal on Mathematical Analysis, Volume 46 (Number 2). pp. 1317-1347. ISSN 0036-1410

2013

Ortner, Christoph and Wang, Hoa. (2013) A posteriori error control for a quasi-continuum approximation of a periodic chain. IMA Journal of Numerical Analysis, Volume 34 (Number 3). pp. 977-1001. ISSN 0272-4979

Luskin, Mitchell Barry, 1951- and Ortner, Christoph. (2013) Atomistic-to-continuum coupling. Acta Numerica, Volume 22 . pp. 397-508. ISSN 0962-4929

Ortner, Christoph and Shapeev, A. V.. (2013) Analysis of an energy-based atomistic/continuum approximation of a vacancy in the 2D triangular lattice. Mathematics of Computation, Volume 82 (Number 284). pp. 2191-2236. ISSN 0025-5718

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

Burke, Siobhan, Ortner, Christoph and Süli, Endre. (2013) An adaptive finite element approximation of a generalized Ambrosio-Tortorelli functional. Mathematical Models and Methods in Applied Sciences, Volume 23 (Number 9). pp. 1663-1697. ISSN 0218-2025

Burke, Siobhan, Ortner, Christoph and Süli, Endre. (2013) An adaptive finite element approximation of a generalized Amrosio-Tortorelli functional. Mathematical Models and Methods in Applied Sciences, Volume 23 (Number 9). pp. 1663-1697. ISSN 0218-2025

Luskin, Mitchell Barry, 1951-, Ortner, Christoph and Van Koten, B.. (2013) Formulation and optimization of the energy-based blended quasicontinuum method. Computer Methods in Applied Mechanics and Engineering, Volume 253 (Number 1). pp. 160-168. ISSN 0045-7825

Jayawardana, Kavinda, Mordacq, Christelle, Ortner, Christoph and Park, Harold S.. (2013) An analysis of the boundary layer in the 1D surface Cauchy–Born model. ESAIM: Mathematical Modelling and Numerical Analysis, Volume 47 (Number 1). pp. 109-123. ISSN 0764-583X

Luskin, Mitchell Barry, 1951- and Ortner, Christoph (2013) Atomistic-to-continuum coupling. In: Engquist, Björn , (ed.) Encyclopedia of Applied and Computational Mathematics. Berlin Heidelberg: Springer Reference, pp. 1-14.

Langwallner, Bernhard, Ortner, Christoph and Süli, Endre. (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

Koten, Brian Van and Ortner, Christoph. (2013) Symmetries of 2-lattices and second order accuracy of the Cauchy-Born model. Multiscale Modeling & Simulation, Volume 11 (Number 2). pp. 615-634. ISSN 1540-3459

2012

Ortner, Christoph and Zhang, L.. (2012) Construction and sharp consistency estimates for atomistic/continuum coupling methods with general interfaces : a two-dimensional model problem. SIAM Journal on Numerical Analysis, Volume 50 (Number 6). pp. 2940-2965. ISSN 0036-1429

Dobson, Matthew, Ortner, Christoph and Shapeev, A. V. . (2012) The spectrum of the force-based quasicontinuum operator for a homogeneous periodic chain. Multiscale Modeling & Simulation, Volume 10 (Number 3). pp. 744-765. 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 (No.1204.3705v1).

Ortner, Christoph and Süli, Endre (2012) A note on linear elliptic systems on $\R^d$. Working Paper. ArXiv e-prints. ArXiv e-prints (No.1202.3970v3).

Ortner, Christoph and Theil, F. (2012) Nonlinear elasticity from atomistic mechanics. Working Paper. ArXiv e-prints. ArXiv e-prints (No.1202.3858v3).

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 (No.1203.5854v1).

Ortner, Christoph. (2012) The role of the patch test in 2D atomistic-to-continuum coupling methods. ESAIM: Mathematical Modelling and Numerical Analysis, Volume 46 (Number 6). pp. 1275-1319. ISSN 0764-583X

Hudson, Thomas and Ortner, Christoph. (2012) On the stability of Bravais lattices and their Cauchy–Born approximations. ESAIM: Mathematical Modelling and Numerical Analysis, Volume 46 (Number 1). pp. 81-110. ISSN 0764-583X

Luskin, Mitchell Barry, 1951- and Ortner, Christoph (2012) Linear stationary iterative methods for the force-based quasicontinuum approximation. In: Engquist, Björn, 1945- and Runborg, Olof and Tsai, Yen-Hsi R., (eds.) Numerical Analysis of Multiscale Computations. Lecture notes in computational science and engineering, Volume 82 . Berlin: Springer, pp. 331-368. ISBN 9783642219429

Li, Xingjie Helen, Luskin, Mitchell Barry, 1951- and Ortner, Christoph. (2012) Positive definiteness of the blended force-based quasicontinuum method. Multiscale Modeling & Simulation, Volume 10 (Number 3). pp. 1023-1045. ISSN 1540-3459

Makridakis, C., Ortner, Christoph and Süli, Endre. (2012) Stress-based atomistic/continuum coupling : a new variant of the quasicontinuum approximation. International Journal for Multiscale Computational Engineering, Volume 10 (Number 1). pp. 51-64. ISSN 1543-1649

Koten, Brian Van, Li, Xingjie Helen, Luskin, Mitchell Barry, 1951- and Ortner, Christoph (2012) 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, 1972-, (eds.) Numerical analysis of multiscale problems. Lecture notes in computational science and engineering, Volume 83 . Berlin: Springer, pp. 67-96. ISBN 9783642220609

2011

Li, Xingjie Helen, Luskin, Mitchell Barry, 1951- and Ortner, Christoph (2011) Positive-definiteness of the blended force-based quasicontinuum method. Working Paper. ArXiv e-prints. ArXiv e-prints (No.1112.2528v1).

Langwallner, Bernhard, Ortner, Christoph and Süli, Endre (2011) Atomistic-to-continuum coupling approximation of a one-dimensional toy model for density functional theory. Working Paper. ArXiv e-prints. ArXiv e-prints (No.1112.0746v1).

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 (No.1112.0683v1).

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 (No.1110.0168v1).

Dobson, Matthew, Luskin, Mitchell Barry, 1951- 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, Volume 200 (Number 37-40). pp. 2697-2709. ISSN 0045-7825

Makridakis , C. , Ortner, Christoph and Süli, Endre. (2011) A priori error analysis of two force-based atomistic/continuum models of a periodic chain. Numerische Mathematik, Volume 119 (Number 1). pp. 83-121. ISSN 0029-599X

Ortner, Christoph. (2011) Nonconforming finite-element discretization of convex variational problems. IMA Journal of Numerical Analysis, Volume 31 (Number 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, Volume 118 (Number 3). pp. 587-600. ISSN 0029-599X

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, Volume 49 (Number 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, Volume 49 (Number 1). pp. 110-134. ISSN 0036-1429

Ortner, Christoph. (2011) A priori and a posteriori analysis of the quasinonlocal quasicontinuum method in 1D. Mathematics of Computation, Volume 80 (Number 275). pp. 1265-1285. ISSN 0025-5718

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, Volume 21 (Number 12). pp. 2491-2521. ISSN 0218-2025

2010

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, Volume 20 (Number 12). pp. 2237-2265. ISSN 0218-2025

Dobson, Matthew, Luskin, Mitchell Barry, 1951- and Ortner, Christoph. (2010) Accuracy of quasicontinuum approximations near instabilities. Journal of the Mechanics and Physics of Solids, Volume 58 (Number 10). pp. 1741-1757. ISSN 0022-5096

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, Volume 48 (Number 3). pp. 980-1012. ISSN 0036-1429

Larsen, Christopher J., Ortner, Christoph and Süli, Endre. (2010) Existence of solutions to a regularized model of dynamic fracture. Mathematical Models and Methods in Applied Sciences, Volume 20 (Number 7). pp. 1021-1048. ISSN 0218-2025

Dobson, Matthew, Luskin, Mitchell Barry, 1951- and Ortner, Christoph. (2010) Stability, instability, and error of the force-based quasicontinuum approximation. Archive for Rational Mechanics and Analysis, Volume 197 (Number 1). pp. 179-202. ISSN 0003-9527

Dobson, Matthew, 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 (No.1004.3435v1).

Dobson, Matthew, Luskin, Mitchell Barry, 1951- and Ortner, Christoph. (2010) Sharp stability estimates for the force-based quasicontinuum approximation of homogeneous tensile deformation. Multiscale Modeling & Simulation, Volume 8 (Number 3). pp. 782-802. ISSN 1540-3459

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, Volume 10 (Number 2). pp. 137-163. ISSN 1609-4840

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 (No.29). (Unpublished)

2009

Buffa, Annalisa and Ortner, Christoph. (2009) Compact embeddings of broken Sobolev spaces and applications. IMA Journal of Numerical Analysis, Volume 29 (Number 4). pp. 827-855. ISSN 0272-4979

Luskin, Mitchell Barry, 1951- and Ortner, Christoph. (2009) An analysis of node-based cluster summation rules in the quasicontinuum method. SIAM Journal on Numerical Analysis, Volume 47 (Number 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

2008

Negri, Matteo and Ortner, Christoph. (2008) Quasi-static crack propagation by Griffith's criterion. Mathematical Models and Methods in Applied Sciences, Volume 18 (Number 11). pp. 1895-1925. ISSN 0218-2025

Ferraz-Leite, S., Ortner, Christoph and Praetorius, Dirk. (2008) Convergence of simple adaptive Galerkin schemes based on h − h/2 error estimators. Numerische Mathematik, Volume 116 (Number 2). pp. 291-316. ISSN 0029-599X

Ortner, Christoph and Süli, Endre. (2008) Analysis of a quasicontinuum method in one dimension. ESAIM: Mathematical Modelling and Numerical Analysis, Volume 42 (Number 1). pp. 57-91. ISSN 0764-583X

2007

Ortner, Christoph and Süli, Endre. (2007) Discontinuous Galerkin finite element approximation of nonlinear second-order elliptic and hyperbolic systems. SIAM Journal on Numerical Analysis, Volume 45 (Number 4). pp. 1370-1397. ISSN 0036-1429

2006

Ortner, Christoph. (2006) Gradient flows as a selection procedure for equilibria of nonconvex energies. SIAM Journal on Mathematical Analysis, Volume 38 (Number 4). pp. 1214-1234. ISSN 0036-1410