- C. Ortner, Gradient flows as a selection criterion. SIAM J. Math. Anal., Volume 38, 2006.
- C. Ortner and E. Süli, Discontinuous Galerkin finite element approximation of nonlinear second-order elliptic and hyperbolic systems. SIAM Journal on Numerical Analysis, Volume 45, Issue 4, pp.1370-1397, July 2007. DOI:10.1137/06067119X
- C. Ortner and E. Süli, Analysis of a quasicontinuum method in one dimension. ESAIM: M2AN, 42 (1), 57–91 (2008).
- J. M. Ball and C. Mora-Corral, A variational model allowing both smooth and sharp phase boundaries in solids. Submitted to Communications on Pure and Applied Analysis.
- A. Buffa and C. Ortner, Variational convergence of IP-DGFEM. IMA J. Numer. Anal. 29(4), 2009.
- M. Negri and C. Ortner, Quasistatic crack propagation by Griffith’s criterion. Math. Models and Methods Appl. Sc., Vol. 18 (2008).
- G.W. Jones, S.J. Chapman, D.J. Allwright, Axisymmetric buckling of a spherical shell embedded in an elastic medium under uniaxial stress at infinity. Submitted to Q. Jl. Mech. Appl. Math., 2007.
- C. Ortner, A-posteriori existence in numerical computations. SIAM J. Numer. Anal. 47(4), 2009.
- C. Ortner, Nonconforming finite element methods for convex variational problems, IMA J. Numer. Anal. 31, 2011
- P. Pathmanathan, J. Whiteley, S.J. Chapman, D. Gavaghan, Predicting Tumour Location by Modelling the Deformation of the Breast. Accepted by IEEE Transactions in Biomedical Engineering.
- P. Pathmanathan, J. Whiteley, A numerical method for modelling coupled electrophysiology and mechanics in the heart. Submitted to Annals of Biomedical Engineering.
- J. Pitt-Francis et al (incl P. Pathmanathan) Chaste: Using agile programming techniques to develop computational biology software. Submitted to Phil Trans of the Royal Soc.
- C. Mora-Corral, Continuum limits of atomistic energies allowing smooth and sharp interfaces in 1D Elasticity. Submitted to Interfaces and Free Boundaries.
- C. Ortner and D. Praetorius, On the convergence of non-conforming finite element methods, SIAM J. Numer. Anal. 49, 2011
- M. Luskin and C. Ortner, An Analysis of Node-Based Cluster Summation Rules in the Quasicontinuum Method. SIAM J. Numer. Anal. 47(4), 2009.
- S. Burke, C. Ortner and E. Süli, An adaptive finite element approximation of a variational model of brittle fracture, SIAM J. Numer. Anal. 48(3), 2010.
- C. Carstensen and C. Ortner, Computation of the Lavrentiev Phenomenon, Computational Methods in Applied Mathematics 2, 2010.
- C.J. Larsen, C. Ortner, and E. Süli, Existence of Solutions to a Regularized Model of Dynamic Fracture. Math. Models Methods Appl. Sc. 20(7), 2010.
- M. Dobson, M. Luskin, and C. Ortner, Stability, Instability, and Error of the Force-based Quasicontinuum Approximation. Arch. Rat. Mech. Anal. 197(1), 2010.
- M. Dobson, M. Luskin, and C. Ortner, Sharp Stability Estimates for the Accurate Prediction of Instabilities by the Quasicontinuum Method, J. Mech. Phys. Solids 58, 2010.
- B. Langwallner, C. Ortner, and E. Süli, Existence and Convergence Results for the Galerkin Approximation of an Electronic Density Functional, Math. Models Methods Appl. Sc. 20, 2010.
- C. Ortner and W. Wollner, Optimal Control with Pointwise Constraints on the Gradient of the State. Numer. Math. 118, 2011.
- M. Dobson, M. Luskin, and C. Ortner, Sharp Stability Estimates for the Force-Based Quasicontinuum Method. SIAM Multiscale Model. Simul. 8(3), 2010.
- M. Dobson, M. Luskin, and C. Ortner, Iterative Methods for the Force-based Quasicontinuum Approximation. Comput. Methods Appl. Mech. Engrg. 200, 2011.
- C. Ortner, A Priori and A Posteriori Analysis of the Quasi-Nonlocal Quasicontinuum Method in 1D. Math. Comp. 80, 2011.
- M. Dobson, C. Ortner and A. Shapeev, The Spectrum of the Force-Based Quasicontinuum Operator for a Homogeneous Periodic Chain. Submitted.
- C. Makridakis, C. Ortner and E. Süli, Stress-Based Atomistic/Continuum Coupling: A New Variant of the Quasicontinuum Approximation. To appear in International Journal for Multiscale Computational Engineering.
- C. Makridakis, C. Ortner and E. Süli, A Priori Error Analysis of two force-based atomistic/continuum hybdrid models of a periodic chain. Numer. Math. 119, 2011.
- S. Burke, C. Ortner and E. Süli, An Adaptive Finite Element Approximation of a Generalised Ambrosio-Tortorelli Functional. Submitted.
- C. Ortner and H. Wang, A Priori Error Estimates for Energy-Based Quasicontinuum Approximations of a Periodic Chain. To appear in M3AS.
- T. Hudson and C. Ortner, On the Stability of Bravais Lattices and their Cauchy-Born Approximations. EASIM:M2AN 46, 2012.
- C. Ortner, The role of the patch test in 2D atomistic-to-continuum coupling methods. Submitted.
- C. Ortner and A. Shapeev, Analysis of an energy-based atomistic/continuum coupling approximation of a vacancy defect in the 2D triangular lattice . Submitted.
- B. Langwallner, C. Ortner, E. S"uli, Quasicontinuum Coupling for a Field-Based Interaction Potential ; Revised Version
- M. Jungen, A Model of Columnar Jointing. Math. Models Methods Appl. Sc. 22(2), 2012.

Note: Please send further reports to the website maintainer.

- C. Ortner and E. Süli. A-posteriori analysis and adaptive algorithms for the quasicontinuum method in one dimension. Report NA-06/13.
- C. Ortner and E. Süli. A-priori analysis of the quasicontinuum method in one dimension. Report NA-06/12.
- C. Ortner. A-posteriori existence in adaptive computations. Report NA-06/11.
- C. Ortner and E. Süli. Discontinuous Galerkin finite element approximation of nonlinear second-order elliptic and hyperbolic systems. Report NA-06/05.
- C. Ortner. Continuum limits of a one-dimensional atomistic energy based on local minimization. Report NA-05/11.
- C. Ortner. Two variational techniques for the approximation of curves of maximal slope. Report NA-05/10.
- C. Ortner. Gamma-limits of Galerkin discretisations with quadrature. Report NA-04/26.