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John Mackenzie's Publications
  1. C.S. MacDonald, J.A. Mackenzie, A. Ramage and C.J.P Newton
    Robust adaptive computation of a one-dimensional Q-tensor model of nematic liquid crystals.
    Strathclyde Mathematics Research Report No. 16, 2011.

  2. J.A. Mackenzie and W.R. Mekwi
    An Unconditionally Stable Second-Order Accurate ALE-FEM Scheme for Two-Dimensional Convection-Diffusion Problems.
    IMA Journal of Numerical Analysis, 2011; doi: 10.1093/imanum/drr021

  3. M.P. Neilson, D.M. Veltman, P.J.M. van Haastert, S.D. Webb, J.A. Mackenzie and R.H. Insall
    Chemotaxis: A Feedback-Based Computational Model Robustly Predicts Multiple Aspects of Real Cell Behaviour.
    PLoS Biology, 9(5):e1000618.doi:10.1371/journal.pbio.1000618, 2011.

  4. M.P. Neilson, J.A. Mackenzie, S.D. Webb and R.H. Insall
    Modelling Cell Movement and Chemotaxis Using Pseudopod-Based Feedback.
    SIAM Journal on Scientific Computing, Vol. 33, pages 1035-1057, 2011.

  5. J.A. Mackenzie and A. Madvamuse
    Analysis of Stability and Convergence of Finite-Difference Methods for a Reaction-Diffusion problem on a One-Dimensional Growing Domain.
    IMA Journal of Numerical Analysis, Vol. 31, pages 212-232, 2011; doi:10.1093/imanum/drp030

  6. M.P. Neilson, J.A. Mackenzie, S.D. Webb and R.H. Insall
    Use of the parameterised finite element method to robustly and efficiently evolve the edge of a moving cell.
    Integrative Biology, Vol. 2, pages 687-695, 2010.

  7. M.T. Stickland, T.J. Scanlon and J.A. Mackenzie.
    An experimental investigation of natural convection with solidification in a differentially heated cavity.
    International Journal of Heat and Mass Transfer, Vol 50, No. 1-2, pages 36--44, 2007.

  8. J.A. Mackenzie and A. Nicola
    A Discontinuous Galerkin Moving Mesh Method for Hamilton-Jacobi Equations.
    SIAM Journal on Scientific Computing, Vol. 29, pages 2258-2282, 2007.

  9. J.A. Mackenzie and W.R. Mekwi
    An analysis of stability and convergence of a finite difference discretisation of a model parabolic PDE in 1D using a moving mesh.
    IMA Journal of Numerical Analysis, Vol. 27, pages 507-528, 2007; doi:10.1093/imanum/drl034

  10. J.A. Mackenzie and W.R. Mekwi
    On the Use of Moving Mesh Methods to Solve PDEs.
    in T. Tang and J. Xu eds., Adaptive Computations: Theory and Algorithms, pages 243-278, Science Press, Beijing, ISBN 978-7-03-018421-4, 2007.

  11. G. Beckett, J.A. Mackenzie and M.L. Robertson.
    An r-Adaptive Finite Element Method for the Solution of the Two-Dimensional Phase-Field Equations.
    Communications in Computational Physics, Vol. 1, No. 5, pages 805--826, 2006.

  12. R.T. Tenchev, J.A. Mackenzie, T.J. Scanlon and M.T. Stickland.
    Finite element moving mesh analysis of phase change problems with natural convection.
    International Journal of Heat and Fluid Flow, Vol. 26, pages 597--612, 2005.

  13. G. Beckett, J.A. Mackenzie, A. Ramage and D.M. Sloan.
    Computational solution of two-dimensional unsteady PDEs using moving mesh methods.
    Journal of Computational Physics, Vol 182, pages 478-495, 2002.

  14. J.A. Mackenzie and M.L. Robertson.
    A moving mesh method for the solution of the one-dimensional phase-field equations.
    Journal of Computational Physics, Vol. 181, No. 2, pages 526-544, 2002.

  15. C. Constanda, J. Kidd, J.A. Mackenzie and I.W. Stewart.
    Connection between liquid crystal theory and plate theory.
    Integral Methods in Science and Engineering, Birkhauser, Boston, pages 137-142, 2002.

  16. G. Beckett and J.A. Mackenzie.
    Uniformly convergent high order finite element solutions of a singularly perturbed reaction-diffusion equation using mesh equidistribution.
    Applied Numerical Mathematics, Vol. 39, No. 1, pages 31-45, 2001.

  17. G. Beckett and J.A. Mackenzie.
    On a uniformly accurate finite difference approximation of a singularly perturbed reaction-diffusion problem using grid equidistribution.
    Journal of Computational and Applied Mathematics, vol. 131, No. 1-2, pages 381-405, 2001.

  18. G. Beckett, J.A. Mackenzie and M.L. Robertson.
    A Moving Mesh Finite Element Method for the Solution of Two-Dimensional Stefan Problems.
    Journal of Computational Physics, vol. 168, No. 2, pages 500-518, 2001.

  19. G. Beckett, J.A. Mackenzie, A. Ramage and D.M. Sloan.
    On the numerical solution of one-dimensional PDEs using adaptive methods based on equidistribution.
    Journal of Computational Physics, Vol. 167, No. 2, pages 372-392, 2001.

  20. J.M. Stockie, J.A. Mackenzie and R.D. Russell.
    A Moving Mesh Method for One-Dimensional Hyperbolic Conservation Laws.
    SIAM Journal on Scientific Computing, Vol 22, No. 5, pages 1791-1813, 2001.

  21. G. Beckett and J.A. Mackenzie.
    Convergence analysis of finite-difference approximations on equidistributed grids to a singularly perturbed boundary value problem.
    Applied Numerical Mathematics, Vol 35, No. 2, pages 109-131, 2000.

  22. J.A.Mackenzie and M.L. Robertson.
    The numerical solution of one-dimensional phase change problems using an adaptive moving mesh method.
    Journal of Computational Physics, Vol. 161, No. 2, pages 537-557, 2000.

  23. P. Houston, J.A. Mackenzie, E.Suli and G.Warnecke.
    A posteriori analysis for numerical approximations of Friedrichs systems.
    Numerische Mathematik Vol. 82, No. 3, pages 433-470, 1999.

  24. J.A. Mackenzie.
    Uniform convergence analysis of an upwind finite-difference approximation of a convection-diffusion boundary value problem on an adaptive grid.
    IMA Journal of Numerical Analysis, Vol. 19, pages 233--249, 1999.

  25. J.A.Mackenzie.
    The Efficient Generation of Simple Two-Dimensional Adaptive Grids.
    SIAM Journal on Scientific Computing. Pages 1340--1365 Volume 19, No. 4. 1998.

  26. J.A.Mackenzie.
    Adaptive finite volume methods.
    Proccedings of the CFD 97 conference, Victoria, Canada, Pages 5-12

  27. B.Garcia-Archilla, and J.A. Mackenzie.
    Analysis of a supraconvergent cell-vertex finite volume method for one-dimensional convection-diffusion problems.
    IMA Journal of Numerical Analysis, Vol. 15, pages 101--115, 1995.

  28. J.A.Mackenzie.
    An investigation of artificial dissipation for the cell-vertex finite volume method.
    International journal for numerical methods in fluids, vol. 21, pages 499-522, 1995.

  29. J.A.Mackenzie and E.Suli.
    Reliable Error Control for Adaptive Computations of the Compressible Euler Equations.
    Numerical Methods for Fluid Dynamics V, Oxford Science Publications, pages 473-479, 1995.

  30. J.A. Mackenzie, E.Suli and G.Warnecke.
    A posteriori error estimates for the cell-vertex finite volume method.
    Notes on Numerical Fluid Mechanics, Vol. 46, pages 221--235, Vieweg, 1994.

  31. J.A.Mackenzie, T. Sonar and E.Suli.
    Adaptive finite volume methods for hyperbolic problems.
    The Mathematics of Finite Elements and Applications, Highlights 1993, pages 289--298, John Wiley & Sons, 1994.

  32. J.A.Mackenzie, D.F. Mayers and A.J. Mayfield.
    Error estimates for adaptive cell vertex finite volume algorithms.
    Numerical Methods for Fluid Dynamics IV, Oxford Science Publications, pages 517-523, 1993.

  33. J.A. Mackenzie, D.F. Mayers and A.J. Mayfield.
    Error estimates and mesh adaption for a cell vertex finite volume scheme.
    Notes on Numerical Fluid Mechanics, Vol. 44, pages 290--310, Vieweg, 1993.

  34. J.A. Mackenzie and K.W. Morton.
    Finite volume solutions of convection-diffusion test problems.
    Mathematics of Computation, Vol 60. pages 189-230, 1993.

  35. P.I. Crumpton, J.A. Mackenzie and K.W. Morton.
    Cell vertex finite volume algorithms for the compressible Navier--Stokes equations.
    Journal of Computational Physics, Vol. 109, pages 1-15, 1993.

  36. P.I. Crumpton, J.A. Mackenzie and K.W. Morton.
    Cell vertex methods for inviscid and viscous flows.
    Computers and Fluids, Vol. 22, No, 2/3, pages 91-102, 1993.

  37. P.I. Crumpton, J.A. Mackenzie, and K.W. Morton.
    A consistent cell vertex finite volume method for the compressible Navier--Stokes equations.
    Lecture Notes in Physics, Vol. 414, pages 519-523, Springer Verlag, 1993.

  38. J.A. Mackenzie.
    An accurate cell vertex finite volume method for the compressible Navier-Stokes equations.
    Proccedings of the Fourth International Symposium on Computational Fluid Dynamics Vol. II, pages 753-758, 1991.

  39. P.I. Crumpton, J.A. Mackenzie,K.W. Morton, M.A. Rudgyard and G.J. Shaw.
    Cell vertex multigrid methods for the compressible Navier--Stokes equations.
    Lecture Notes in Physics, Vol. 371, pages 243-247, Springer Verlag, 1990.


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