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Number of items: 95.
2024
Bachmayr, Markus, Dusson, Geneviève, Ortner, Christoph and Thomas, Jack (2024) Polynomial approximation of symmetric functions. Mathematics of Computation, 93 (346). pp. 811-839. doi:10.1090/mcom/3868 ISSN 0025-5718.
2023
Darby, James P., KovΓ‘cs, DΓ‘vid P., Batatia, Ilyes, Caro, Miguel A., Hart, Gus L. W., Ortner, Christoph and CsΓ‘nyi, GΓ‘bor (2023) Tensor-reduced atomic density representations. Physical Review Letters, 131 (2). 028001. doi:10.1103/PhysRevLett.131.028001 ISSN 0031-9007.
2022
Pozdnyakov, Sergey, Willatt, Michael John, Bartok-Partay, Albert, Ortner, Christoph, Csanyi, Gabor and Ceriotti, Michele (2022) Comment on "Manifolds of quasi-constant SOAP and ACSF fingerprints and the resulting failure to machine learn four body interactions". The Journal of Chemical Physics, 157 . 177101. doi:10.1063/5.0088404 ISSN 1089-7690.
Thomas, Jack, Chen, Huajie and Ortner, Christoph (2022) Body-ordered approximations of atomic properties. Archive for Rational Mechanics and Analysis, 246 . pp. 1-60. doi:10.1007/s00205-022-01809-w ISSN 1432-0673.
Braun, Julian, Hudson, Thomas E. (Edward) and Ortner, Christoph (2022) Asymptotic expansion of the elastic far-field of a crystalline defect. Archive for Rational Mechanics and Analysis, 245 . pp. 1437-1490. doi:10.1007/s00205-022-01810-3 ISSN 0003-9527.
Zhang, Liwei, Onat, Berk, Dusson, Geneviève, McSloy, Adam, Anand, G., Maurer, Reinhard J., Ortner, Christoph and Kermode, James R. (2022) Equivariant analytical mapping of first principles Hamiltonians to accurate and transferable materials models. npj Computational Materials, 8 (1). 158. doi:10.1038/s41524-022-00843-2 ISSN 2057-3960.
2021
Musil, Felix, Grisafi, Andrea, BartΓ³k, Albert P., Ortner, Christoph, CsΓ‘nyi, GΓ‘bor and Ceriotti, Michele (2021) Physics-inspired structural representations for molecules and materials. Chemical Reviews, 121 (16). pp. 9759-9815. doi:10.1021/acs.chemrev.1c00021 ISSN 0009-2665.
2020
Buze, Maciej, Hudson, Thomas E. (Edward) and Ortner, Christoph (2020) Analysis of cell size effects in atomistic crack propagation. ESAIM: Mathematical Modelling and Numerical Analysis, 54 (6). pp. 1821-1847. doi:10.1051/m2an/2020005 ISSN 0764-583X.
Pozdnyakov, Sergey N., Willatt, Michael J., BartΓ³k, Albert P., Ortner, Christoph, Csanyi, Gabor and Ceriotti, Michele (2020) Incompleteness of atomic structure representations. Physical Review Letters, 125 . 166001. doi:10.1103/PhysRevLett.125.166001 ISSN 0031-9007.
Onat, Berk, Ortner, Christoph and Kermode, James R. (2020) Sensitivity and dimensionality of atomic environment representations used for machine learning interatomic potentials. The Journal of Chemical Physics, 153 (14). 144106. doi:10.1063/5.0016005 ISSN 0021-9606.
van der Oord, Cas, Dusson, Geneviève, Csanyi, Gabor and Ortner, Christoph (2020) Regularised atomic body-ordered permutation-invariant polynomials for the construction of interatomic potentials. Machine Learning : Science and Technology, 1 (1). 015004. doi:10.1088/2632-2153/ab527c ISSN 2632-2153.
Braun, Julian and Ortner, Christoph (2020) Sharp uniform convergence rate of the supercell approximation of a crystalline defect. SIAM Journal of Numerical Analysis, 58 (1). pp. 279-297. doi:10.1137/18M122830X ISSN 1095-7170.
2019
Buze, Maciej, Hudson, Thomas E. (Edward) and Ortner, Christoph (2019) Analysis of an atomistic model for anti-plane fracture. Mathematical Models & Methods in Applied Sciences, 29 (13). pp. 2469-2521. doi:10.1142/S0218202519500520 ISSN 0218-2025.
Braun, Julian, Buze, Maciej and Ortner, Christoph (2019) The effect of crystal symmetries on the locality of screw dislocation cores. SIAM Journal of Mathematical Analysis, 51 (2). pp. 1108-1136. doi:10.1137/17M1157520 ISSN 0036-1410.
Chen, Huajie, Nazar, Faizan Q. and Ortner, Christoph (2019) Geometry equilibration of crystalline defects in quantum and atomistic descriptions. Mathematical Models and Methods in Applied Sciences, 29 (03). pp. 419-492. doi:10.1142/S0218202519500131 ISSN 0218-2025.
Makri, Stela, Ortner, Christoph and Kermode, James R. (2019) A preconditioning scheme for minimum energy path finding methods. The Journal of Chemical Physics, 150 (9). 094109. doi:10.1063/1.5064465 ISSN 0021-9606.
2018
Olson, Derek, Li, Xingjie, Ortner, Christoph and Van Koten, Brian (2018) Force-based atomistic/continuum blending for multilattices. Numerische Mathematik, 140 (3). pp. 703-754. doi:10.1007/s00211-018-0979-x ISSN 0029-599X.
Chen, Huajie, Lu, Jianfeng and Ortner, Christoph (2018) Thermodynamic limit of crystal defects with finite temperature tight binding. Archive for Rational Mechanics and Analysis, 230 (2). pp. 701-733. doi:10.1007/s00205-018-1256-y ISSN 0003-9527.
Mones, Letif, Ortner, Christoph and CsΓ‘nyi, GΓ‘bor (2018) Preconditioners for the geometry optimisation and saddle point search of molecular systems. Scientific Reports, 8 (1). 13991 . doi:10.1038/s41598-018-32105-x ISSN 2045-2322.
Dobson, Matthew, Duong, Manh Hong and Ortner, Christoph (2018) On assessing the accuracy of defect free energy computations. ESAIM: Mathematical Modelling and Numerical Analysis, 52 (4). pp. 1315-1352. doi:10.1051/m2an/2017052 ISSN 0764-583X.
Massatt, D., Carr, S., Luskin, M. and Ortner, Christoph (2018) Incommensurate heterostructures in momentum space. Multiscale Modelling and Simulation : A SIAM Interdisciplinary Journal , 16 (1). pp. 429-451. doi:10.1137/17M1141035 ISSN 1540-3459.
AlRachid, H., Mones, Letif and Ortner, Christoph (2018) Some remarks on preconditioning molecular dynamics. SMAI Journal of Computational Mathematics, 4 . pp. 57-80. doi:10.5802/smai-jcm.29 ISSN 2426-8399.
2017
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:10.1051/m2an/2017013 ISSN 0764-583X.
Levitt, Antoine and Ortner, Christoph (2017) Convergence and cycling in Walker-type saddle search algorithms. SIAM Journal on Numerical Analysis, 55 (5). pp. 2204-2227. doi:10.1137/16M1087199 ISSN 0036-1429.
Olson, Derek and Ortner, Christoph (2017) Regularity and locality of point defects in multilattices. Applied Mathematics Research eXpress, 2017 (2). pp. 297-337. doi:10.1093/amrx/abw012 ISSN 1687-1200.
PΓ‘rtay, LΓvia B., Ortner, Christoph, BartΓ³k, Albert P., Pickard, Chris J. and CsΓ‘nyi, GΓ‘bor (2017) Polytypism in the ground state structure of the Lennard-Jonesium. Physical Chemistry Chemical Physics, 19 . pp. 19369-19376. doi:10.1039/c7cp02923c ISSN 1463-9076.
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 ISSN 1540-3459.
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. doi:10.1137/16M1088363 ISSN 1540-3459.
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 ISSN 0003-9527.
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 ISSN 0029-599X.
Nazar, Faizan Q. and Ortner, Christoph (2016) Locality of the Thomas-Fermi-von WeizsΓ€cker Equations. Archive for Rational Mechanics and Analysis, 224 (3). 817. doi:10.1007/s00205-017-1075-6 ISSN 0003-9527.
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 ISSN 0021-9606.
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 ISSN 0025-5718.
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 ISSN 1540-3459.
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 ISSN 1064-8275 .
2015
Hudson, Thomas and Ortner, Christoph (2015) Analysis of stable screw dislocation configurations in an antiplane lattice model. SIAM Journal on Mathematical Analysis, 47 (1). pp. 291-320. doi:10.1137/140964436 ISSN 0036-1410.
2014
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 , 12 (3). pp. 1258-1293. doi:10.1137/130933873 ISSN 1540-3459.
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 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, 213 (3). pp. 887-929. doi:10.1007/s00205-014-0746-9 ISSN 0003-9527.
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 ISSN 0045-7825.
Mielke, Alexander, Ortner, Christoph and ΕengΓΌl, 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 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. doi:10.1093/imanum/drt011 ISSN 0272-4979.
Luskin, Mitchell Barry and Ortner, Christoph (2013) Atomistic-to-continuum coupling. Acta Numerica, Volume 22 . pp. 397-508. doi:10.1017/S0962492913000068 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. doi:10.1090/S0025-5718-2013-02687-7 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. doi:10.1007/s00205-012-0592-6 ISSN 0003-9527.
Burke, Siobhan, Ortner, Christoph and SΓΌli, 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 ISSN 0218-2025.
Burke, Siobhan, Ortner, Christoph and SΓΌli, 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 ISSN 0218-2025.
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 ISSN 0045-7825.
Jayawardana, Kavinda, Mordacq, Christelle, Ortner, Christoph and Park, Harold S. (2013) An analysis of the boundary layer in the 1D surface CauchyβBorn model. ESAIM: Mathematical Modelling and Numerical Analysis, Volume 47 (Number 1). pp. 109-123. doi:10.1051/m2an/2012021 ISSN 0764-583X.
Luskin, Mitchell Barry and Ortner, Christoph (2013) Atomistic-to-continuum coupling. In: Engquist, BjΓΆrn , (ed.) Encyclopedia of Applied and Computational Mathematics. Berlin Heidelberg: Springer Reference, pp. 1-14.
Langwallner, Bernhard, Ortner, Christoph and SΓΌli, 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 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. doi:10.1137/120870220 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. doi:10.1137/110851791 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. doi:10.1137/110825704 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 SΓΌli, 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, Florian (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 ISSN 0764-583X.
Hudson, Thomas and Ortner, Christoph (2012) On the stability of Bravais lattices and their CauchyβBorn approximations. ESAIM: Mathematical Modelling and Numerical Analysis, Volume 46 (Number 1). pp. 81-110. doi:10.1051/m2an/2011014 ISSN 0764-583X.
Luskin, Mitchell Barry and Ortner, Christoph (2012) Linear stationary iterative methods for the force-based quasicontinuum approximation. In: Engquist, BjΓΆrn, 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 ISSN 1540-3459.
Makridakis, C., Ortner, Christoph and SΓΌli, 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 ISSN 1543-1649.
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 SΓΌli, 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 ISSN 0045-7825.
Makridakis , C. , Ortner, Christoph and SΓΌli, 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 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. doi:10.1093/imanum/drq004 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. doi:10.1007/s00211-011-0360-9 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. doi:10.1137/090781073 ISSN 0036-1429.
Bartels, SΓΆren, MΓΌller, RΓΌdiger and Ortner, Christoph (2011) Robust a priori and a posteriori error analysis for the approximation of AllenβCahn and GinzburgβLandau equations past topological changes. SIAM Journal on Numerical Analysis, Volume 49 (Number 1). pp. 110-134. doi:10.1137/090751530 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. doi:10.1090/S0025-5718-2010-02453-6 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. doi:10.1142/S0218202511005817 ISSN 0218-2025.
2010
Langwallner, Bernhard, Ortner, Christoph and SΓΌli, 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 ISSN 0218-2025.
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 ISSN 0022-5096.
Burke, Siobhan, Ortner, Christoph and SΓΌli, 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 ISSN 0036-1429.
Larsen, Christopher J., Ortner, Christoph and SΓΌli, 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 ISSN 0218-2025.
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 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 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 ISSN 1540-3459.
Burke, Siobhan, Ortner, Christoph and SΓΌli, Endre (2010) Adaptive finite element approximation of the FrancfortβMarigo 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 SΓΌli, Endre (2010) An adaptive finite element approximation of a generalised ambrosioβtortorelli 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 ISSN 0272-4979.
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 ISSN 0036-1429.
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 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. doi:10.1142/S0218202508003236 ISSN 0218-2025.
Ferraz-Leite, S., Ortner, Christoph and Praetorius, Dirk (2008) Convergence of simple adaptive Galerkin schemes based on h β h/2 error estimators. Numerische Mathematik, Volume 116 (Number 2). pp. 291-316. doi:10.1007/s00211-010-0292-9 ISSN 0029-599X.
Ortner, Christoph and SΓΌli, 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 ISSN 0764-583X.
2007
Ortner, Christoph and SΓΌli, 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 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. doi:10.1137/050643982 ISSN 0036-1410.
This list was generated on Tue Mar 19 07:03:25 2024 GMT.