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Reports

OxMOS Preprint Series

  1. C. Ortner, Gradient flows as a selection criterion. SIAM J. Math. Anal., Volume 38, 2006.
  2. 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
  3. C. Ortner and E. Süli, Analysis of a quasicontinuum method in one dimension. ESAIM: M2AN, 42 (1), 57–91 (2008).
  4. 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.
  5. A. Buffa and C. Ortner, Variational convergence of IP-DGFEM. IMA J. Numer. Anal. 29(4), 2009.
  6. M. Negri and C. Ortner, Quasistatic crack propagation by Griffith’s criterion. Math. Models and Methods Appl. Sc., Vol. 18 (2008).
  7. 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.
  8. C. Ortner, A-posteriori existence in numerical computations. SIAM J. Numer. Anal. 47(4), 2009.
  9. C. Ortner, Nonconforming finite element methods for convex variational problems, IMA J. Numer. Anal. 31, 2011
  10. 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.
  11. P. Pathmanathan, J. Whiteley, A numerical method for modelling coupled electrophysiology and mechanics in the heart. Submitted to Annals of Biomedical Engineering.
  12. 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.
  13. C. Mora-Corral, Continuum limits of atomistic energies allowing smooth and sharp interfaces in 1D Elasticity. Submitted to Interfaces and Free Boundaries.
  14. C. Ortner and D. Praetorius, On the convergence of non-conforming finite element methods, SIAM J. Numer. Anal. 49, 2011
  15. M. Luskin and C. Ortner, An Analysis of Node-Based Cluster Summation Rules in the Quasicontinuum Method. SIAM J. Numer. Anal. 47(4), 2009.
  16. 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.
  17. C. Carstensen and C. Ortner, Computation of the Lavrentiev Phenomenon, Computational Methods in Applied Mathematics 2, 2010.
  18. 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.
  19. M. Dobson, M. Luskin, and C. Ortner, Stability, Instability, and Error of the Force-based Quasicontinuum Approximation. Arch. Rat. Mech. Anal. 197(1), 2010.
  20. 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.
  21. 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.
  22. C. Ortner and W. Wollner, Optimal Control with Pointwise Constraints on the Gradient of the State. Numer. Math. 118, 2011.
  23. M. Dobson, M. Luskin, and C. Ortner, Sharp Stability Estimates for the Force-Based Quasicontinuum Method. SIAM Multiscale Model. Simul. 8(3), 2010.
  24. M. Dobson, M. Luskin, and C. Ortner, Iterative Methods for the Force-based Quasicontinuum Approximation. Comput. Methods Appl. Mech. Engrg. 200, 2011.
  25. C. Ortner, A Priori and A Posteriori Analysis of the Quasi-Nonlocal Quasicontinuum Method in 1D. Math. Comp. 80, 2011.
  26. M. Dobson, C. Ortner and A. Shapeev, The Spectrum of the Force-Based Quasicontinuum Operator for a Homogeneous Periodic Chain. Submitted.
  27. 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.
  28. 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.
  29. S. Burke, C. Ortner and E. Süli, An Adaptive Finite Element Approximation of a Generalised Ambrosio-Tortorelli Functional. Submitted.
  30. C. Ortner and H. Wang, A Priori Error Estimates for Energy-Based Quasicontinuum Approximations of a Periodic Chain. To appear in M3AS.
  31. T. Hudson and C. Ortner, On the Stability of Bravais Lattices and their Cauchy-Born Approximations. EASIM:M2AN 46, 2012.
  32. C. Ortner, The role of the patch test in 2D atomistic-to-continuum coupling methods. Submitted.
  33. C. Ortner and A. Shapeev, Analysis of an energy-based atomistic/continuum coupling approximation of a vacancy defect in the 2D triangular lattice . Submitted.
  34. B. Langwallner, C. Ortner, E. S"uli, Quasicontinuum Coupling for a Field-Based Interaction Potential ; Revised Version
  35. M. Jungen, A Model of Columnar Jointing. Math. Models Methods Appl. Sc. 22(2), 2012.

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