2018

Ortner, Christoph, Alrachid, H. and Mones, Letif (2018) Some remarks on preconditioning molecular dynamics. SMAI Journal of Computational Mathematics . (In Press)

2017

Massatt, D., Carr, S., Luskin, M. and Ortner, Christoph (2017) Incommensurate heterostructures in momentum space. Multiscale Modelling and Simulation : A SIAM Interdisciplinary Journal . (In Press)

Dedner, Andreas, Ortner, Christoph and Wu, H. (2017) Analysis of patch-test consistent atomistic-to-continuum coupling with higher-order finite elements. ESAIM: Mathematical Modelling and Numerical Analysis, 51 (6). pp. 2263-2288. doi:10.1016/j.epidem.2017.04.001

Dobson, Matthew, Duong, Manh Hong and Ortner, Christoph (2017) On assessing the accuracy of defect free energy computations. ESAIM: Mathematical Modelling and Numerical Analysis . doi:10.1051/m2an/2017052 (In Press)

Pártay, Lívia B., Ortner, Christoph, Bartók, Albert P., Pickard, Chris J. and Csányi, Gábor (2017) Polytypism in the ground state structure of the Lennard-Jonesium. Physical Chemistry Chemical Physics, 19 . pp. 19369-19376. doi:10.1039/c7cp02923c

Levitt, Antoine and Ortner, Christoph (2017) Convergence and cycling in Walker-type saddle search algorithms. SIAM Journal on Numerical Analysis . (In Press)

Massatt, D., Luskin, M. and Ortner, Christoph (2017) Electronic density of states for incommensurate layers. Multiscale Modeling and Simulation : A SIAM Interdisciplinary Journal, 15 (1). pp. 476-499.

Chen, Huajie and Ortner, Christoph (2017) QM/MM methods for crystalline defects. Part 2 : Consistent energy and force-mixing. Multiscale Modeling & Simulation, 15 (1). pp. 184-214. doi:10.1137/15M1041250

Olson, Derek and Ortner, Christoph (2017) Regularity and locality of point defects in multilattices. Applied Mathematics Research eXpress . pp. 1-41. doi:10.1093/amrx/abw012 (In Press)

2016

Ehrlacher, V., Ortner, Christoph and Shapeev, A. V. (2016) Analysis of boundary conditions for crystal defect atomistic simulations. Archive for Rational Mechanics and Analysis, 222 (3). pp. 1217-1268. doi:10.1007/s00205-016-1019-6

Li, Xingjie Helen, Ortner, Christoph, Shapeev, Alexander V. and Van Koten, Brian (2016) Analysis of blended atomistic/continuum hybrid methods. Numerische Mathematik, 134 (2). pp. 275-326. doi:10.1007/s00211-015-0772-z

Nazar, Faizan Q. and Ortner, Christoph (2016) Locality of the Thomas-Fermi-von Weizsäcker Equations. Archive for Rational Mechanics and Analysis, 224 (3). 817. doi:10.1007/s00205-017-1075-6

Packwood, David, Kermode, James R., Mones, Letif, Bernstein, Noam, Woolley, John, Gould, Nicholas, Ortner, Christoph and Csanyi, Gabor (2016) Data for A universal preconditioner for simulating condensed phase materials. [Dataset]

Packwood, David, Kermode, James R., Mones, Letif, Bernstein, Noam, Woolley, John, Gould, Nicholas, Ortner, Christoph and Csanyi, Gabor (2016) A universal preconditioner for simulating condensed phase materials. Journal of Chemical Physics, 144 (16). 164109. doi:10.1063/1.4947024

Gould, Nicholas, Ortner, Christoph and Packwood, David (2016) A dimer-type saddle search algorithm with preconditioning and linesearch. Mathematics of Computation, 85 . pp. 2939-2966. doi:10.1090/mcom/3096

Chen, Huajie and Ortner, Christoph (2016) QM/MM methods for crystalline defects. Part 1 : Locality of the tight binding model. Multiscale Modeling & Simulation, 14 (1). pp. 232-264. doi:10.1137/15M1022628

Ortner, Christoph and Zhang, Lei (2016) Atomistic/Continuum blending with ghost force correction. SIAM Journal Scientific Computing, 38 (1). A346-A375. doi:10.1137/15M1020241

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. doi:10.1016/j.cma.2014.06.019

Hudson, Thomas and Ortner, Christoph (2014) Existence and stability of a screw dislocation under anti-plane deformation. Archive for Rational Mechanics and Analysis, 213 (3). pp. 887-929. doi:10.1007/s00205-014-0746-9

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 . (Submitted)

Li, Xingjie Helen, Luskin, Mitchell Barry, 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. doi:10.1016/j.cma.2013.10.007

Mielke, Alexander, 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. doi:10.1137/130927632

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. doi:10.1093/imanum/drt011

Luskin, Mitchell Barry and Ortner, Christoph (2013) Atomistic-to-continuum coupling. Acta Numerica, Volume 22 . pp. 397-508. doi:10.1017/S0962492913000068

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. doi:10.1090/S0025-5718-2013-02687-7

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. doi:10.1007/s00205-012-0592-6

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. doi:10.1142/S021820251350019X

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. doi:10.1142/S021820251350019X

Luskin, Mitchell Barry, 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. doi:10.1016/j.cma.2012.09.007

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. doi:10.1051/m2an/2012021

Luskin, Mitchell Barry 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. doi:10.1137/110857787

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. doi:10.1137/120870220

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. doi:10.1137/110851791

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. doi:10.1137/110825704

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. doi:10.1051/m2an/2012005

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. doi:10.1051/m2an/2011014

Luskin, Mitchell Barry 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 and Ortner, Christoph (2012) Positive definiteness of the blended force-based quasicontinuum method. Multiscale Modeling & Simulation, Volume 10 (Number 3). pp. 1023-1045. doi:10.1137/110859270

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. doi:10.1615/IntJMultCompEng.2011002388

Koten, Brian Van, Li, Xingjie Helen, Luskin, Mitchell Barry 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 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 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. doi:10.1016/j.cma.2010.07.008

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. doi:10.1007/s00211-011-0380-5

Ortner, Christoph (2011) Nonconforming finite-element discretization of convex variational problems. IMA Journal of Numerical Analysis, Volume 31 (Number 3). pp. 847-864. doi:10.1093/imanum/drq004

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. doi:10.1007/s00211-011-0360-9

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. doi:10.1137/090781073

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. doi:10.1137/090751530

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. doi:10.1090/S0025-5718-2010-02453-6

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. doi:10.1142/S0218202511005817

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. doi:10.1142/S021820251000491X

Dobson, Matthew, Luskin, Mitchell Barry 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. doi:10.1016/j.jmps.2010.06.011

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. doi:10.1137/080741033

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. doi:10.1142/S0218202510004520

Dobson, Matthew, Luskin, Mitchell Barry 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. doi:10.1007/s00205-009-0276-z

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 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. doi:10.1137/090767005

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.

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. doi:10.1093/imanum/drn038

Luskin, Mitchell Barry 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. doi:10.1137/080743391

Ortner, Christoph (2009) A posteriori existence in numerical computations. SIAM Journal on Numerical Analysis, Vol.47 (No.4). pp. 2550-2577. doi:10.1137/060668183

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. doi:10.1142/S0218202508003236

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. doi:10.1007/s00211-010-0292-9

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. doi:10.1051/m2an:2007057

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. doi:10.1137/06067119X

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. doi:10.1137/050643982