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John Mackenzie's Publications
  1. J. Devlin, D. Husmeier and J.A. Mackenzie
    Optimal estimation of drift and diffusion coefficients in the presence of static localization error
    Physical Review E, 2019.

  2. J.A. Mackenzie and W.R. Mekwi
    An hr-adaptive method for the cubic nonlinear Schrödinger equation
    Journal of Computational and Applied Mathematics, 2019.

  3. J.A. Mackenzie, M. Nolan, C.F. Rowlatt and R.H. Insall
    An adaptive moving mesh method for forced curve shortening flow
    SIAM Journal on Scientific Computing 41 (2), A1170-A1200, 2019.

  4. D. Cusseddu, L. Edelstein-Keshet, J.A. Mackenzie, S. Portet and A. Madzvamuse
    A coupled bulk-surface model for cell polarisation
    Journal of Theoretical Biology, 2018.

  5. A. Mills, N. Wells, J.A. Mackenzie and G. MacDonald
    Kinetics of reduction of a resazurin-based photocatalytic activity ink
    Catalysis Today, Vol. 281, Part 1, pages 14-20, 2017.

  6. J.A. Mackenzie, M. Nolan and R.H. Insall
    Local modulation of chemoattractant concentrations by single cells: dissection using a bulk-surface computational model
    The Royal Society Interface Focus, Vol. 6: 20160036, 2016.

  7. G. MacDonald, J.A. Mackenzie, M. Nolan and R.H. Insall
    A computational method for the coupled solution of reaction-diffusion equations on evolving domains and manifolds: application to a model of cell migration and chemotaxis
    Journal of Computational Physics, Vol. 309, pages 207-226, 2016.

  8. C.S. MacDonald, J.A. Mackenzie, A. Ramage and C.J.P Newton
    Efficient moving mesh methods for Q-tensor models of nematic liquid crystals
    SIAM Journal on Scientific Computing, Vol. 37, No. 2, pages B215-B238, 2015.

  9. 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.
    Computers and Mathematics with Applications, Vol. 64, pages 3627-3640, 2012, doi:10.1016/j.camwa.2012.10.003

  10. 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, Vol 32(3), pages 888-905, 2012; doi: 10.1093/imanum/drr021

  11. 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.

  12. 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.

  13. 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

  14. 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.

  15. 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.

  16. 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.

  17. 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

  18. 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.

  19. 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.

  20. 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.

  21. 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.

  22. 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.

  23. 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.

  24. 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.

  25. 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.

  26. 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.

  27. 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.

  28. 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.

  29. 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.

  30. 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.

  31. 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.

  32. 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.

  33. 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.

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

  35. 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.

  36. 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.

  37. 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.

  38. 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.

  39. 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.

  40. 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.

  41. 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.

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

  43. 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.

  44. 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.

  45. 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.

  46. 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.

  47. 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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