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Article

MacKenzie, John and Rowlatt, Christopher and Insall, Robert (2021) A conservative finite element ALE scheme for mass-conservative reaction-diffusion equations on evolving two-dimensional domains. SIAM Journal on Scientific Computing, 43 (1). B132-B166. ISSN 1064-8275

MacDonald, Craig S. and MacKenzie, John A. and Ramage, Alison (2020) A moving mesh method for modelling defects in nematic liquid crystals. Journal of Computational Physics: X, 8. 100065. ISSN 2590-0552

MacKenzie, J.A. and Mekwi, W.R. (2020) An hr-adaptive method for the cubic nonlinear Schrödinger equation. Journal of Computational and Applied Mathematics, 364. 112320. ISSN 0377-0427

Cusseddu, D. and Edelstein-Keshet, L. and MacKenzie, J.A. and Portet, S. and Madzvamuse, A. (2019) A coupled bulk-surface model for cell polarisation. Journal of Theoretical Biology, 481. pp. 119-135. ISSN 0022-5193

Devlin, J. and Husmeier, D. and MacKenzie, J. A. (2019) Optimal estimation of drift and diffusion coefficients in the presence of static localization error. Physical Review E, 100 (2). 022134. ISSN 2470-0053

Mackenzie, J. A. and Nolan, M. and Rowlatt, C. F. and Insall, R. H. (2019) An adaptive moving mesh method for forced curve shortening flow. SIAM Journal on Scientific Computing, 41 (2). A1170–A1200. ISSN 1064-8275

MacKenzie, John and MacDonald, Grant and Mills, Andrew and Wells, Nathan (2017) Kinetics of reduction of a Resazurin-based photocatalytic activity ink. Catalysis Today, 281 (1). pp. 14-20. ISSN 0920-5861

Mackenzie, J.A. and Nolan, M. and Insall, R.H. (2016) Local modulation of chemoattractant concentrations by single cells : dissection using a bulk-surface computational model. Interface Focus, 6. 20160036. ISSN 2042-8898

MacDonald, G. and MacKenzie, J.A. and Nolan, M. and Insall, R.H. (2016) 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, 309. 207–226. ISSN 0021-9991

MacDonald, Craig S. and MacKenzie, John A. and Ramage, Alison and Newton, Christopher J. P. (2015) Efficient moving mesh methods for Q-tensor models of nematic liquid crystals. SIAM Journal on Scientific Computing, 37 (2). B215-B238. ISSN 1064-8275

MacDonald, Craig and MacKenzie, John and Ramage, Alison and Newton, Chris (2012) Robust adaptive computation of a one-dimensional Q-tensor model of nematic liquid crystals. Computers and Mathematics with Applications, 64 (11). pp. 3627-3640. ISSN 0898-1221

Mackenzie, John and Mekwi, W.R. (2012) An unconditionally stable second-order accurate ALE–FEM scheme for two-dimensional convection–diffusion problems. IMA Journal of Numerical Analysis, 32 (3). pp. 888-905. ISSN 0272-4979

Neilson, Matthew P. and Veltmahn, Douwe M. and van Haastert, Peter J.M. and Webb, Steven and Mackenzie, John A. and Insall, Robert H. (2011) Chemotaxis : a feedback-based computational model robustly predicts multiple aspects of real cell behaviour. PLOS Biology, 9 (5). e1000618.

Mackenzie, J.A. and Madzvamuse, A. (2011) 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, 31 (1). pp. 212-232. ISSN 0272-4979

Neilson, Matthew Paterson and Mackenzie, John and Webb, Steven and Insall, Robert H. (2011) Modelling cell movement and chemotaxis pseudopod based feedback. SIAM Journal on Scientific Computing, 33 (3). 1035–1057. ISSN 1064-8275

Neilson, Matthew Paterson and Mackenzie, John and Webb, Steven and Insall, Robert H. (2010) Use of the parameterised finite element method to robustly and efficiently evolve the edge of a moving cell. Integrative Biology, 2 (11-12). pp. 687-695.

MacKenzie, J.A. and Mekwi, W. (2007) An analysis of stability and convergence of a finite-difference discretization of a model parabolic PDE in 1D using a moving mesh. IMA Journal of Numerical Analysis, 27 (3). pp. 507-528. ISSN 0272-4979

MacKenzie, John and Nicola, Aurelian (2007) A discontinuous Galerkin moving mesh method for Hamilton-Jacobi equations. SIAM Journal on Scientific Computing, 29 (6). pp. 2258-2282. ISSN 1064-8275

Jones, J H and Mackenzie, J and Croft, G A and Beaton, S and Young, D and Donaldson, M D C (2006) Improvement in screening performance and diagnosis of congenital hypothyroidism in Scotland 1979-2003. Archives of Disease in Childhood, 91 (8). pp. 680-685. ISSN 0003-9888

Beckett, G. and MacKenzie, John and Robertson, M.L. (2006) An r-adaptive finite element method for the solution of the two-dimensional phase-field equations. Communications in Computational Physics, 1 (5). pp. 805-826. ISSN 1815-2406

Tenchev, R.T. and MacKenzie, J.A. and Scanlon, T.J. and Stickland, M.T. (2004) Finite element moving mesh analysis of phase change problems with natural convection. International Journal of Heat and Fluid Flow, 26 (4). pp. 597-612. ISSN 0142-727X

Beckett, G. and Ramage, A. and Sloan, D.M. and Mackenzie, J.A. (2002) Computational solution of two-dimensional unsteady PDEs using moving mesh methods. Journal of Computational Physics, 182 (2). pp. 478-495. ISSN 0021-9991

Mackenzie, J.A. and Robertson, M.L. (2002) A moving mesh method for the solution of the one-dimensional phase-field equations. Journal of Computational Physics, 181 (2). pp. 526-544. ISSN 0021-9991

Beckett, G. and Mackenzie, John A. and Robertson, M.L. (2001) A moving mesh finite element method for the solution of two-dimensional Stefan problems. Journal of Computational Physics, 168 (2). pp. 500-518. ISSN 0021-9991

Mackenzie, John A. (2001) Book review of robust computational techniques for boundary layers. SIAM Review, 43 (3). pp. 563-565. ISSN 0036-1445

Beckett, G. and Mackenzie, J.A. (2001) On a uniformly accurate finite difference approximation of a singularly perturbed reaction-diffusion problem using grid equidistribution. Journal of Computational and Applied Mathematics, 131 (1-2). pp. 381-405. ISSN 0377-0427

Beckett, G. and Ramage, A. and Sloan, D.M. and Mackenzie, J.A. (2001) On the numerical solution of one-dimensional PDEs using adaptive methods based on equidistribution. Journal of Computational Physics, 167 (2). pp. 372-392. ISSN 0021-9991

Beckett, G. and Mackenzie, J.A. (2001) Uniformly convergent high order finite element solutions of a singularly perturbed reaction-diffusion equation using mesh equidistribution. Applied Numerical Mathematics, 39 (1). pp. 31-45. ISSN 0168-9274

Stockie, John M. and MacKenzie, John A. and Russell, Robert D. (2001) A moving mesh method for one-dimensional hyperbolic conservation laws. SIAM Journal on Scientific Computing, 22 (5). pp. 1791-1813. ISSN 1064-8275

Book Section

MacKenzie, John and Mekwi, W.R.; Tao, Tang and Xu, Jinchao, eds. (2006) On the use of moving mesh methods to solve PDEs. In: Adaptive communications. Mathematics Monograph Series . Science Press Beijing, pp. 243-278. ISBN 9787030184214

Kidd, J.E. and Constanda, C. and MacKenzie, John and Stewart, Iain; Constanda, C., ed. (2002) Connection between liquid crystal theory and plate theory. In: Integral Methods in Science and Engineering: Theoretical and Practical Aspects. Birkhauser, Boston, USA. ISBN 0-8176-4213-7

Conference or Workshop Item

Mackenzie, J.A. (2004) On the solution of connective heat transfer problems using an adaptive moving mesh method. In: UNSPECIFIED.

Mackenzie, J.A. (2004) An adaptive moving mesh method with local mesh refinement for singularly perturbed PDEs. In: UNSPECIFIED.

Monograph

MacDonald, Craig and MacKenzie, John and Ramage, Alison and Newton, Chris (2011) Robust adaptive computation of a one-dimensional Q-tensor model of nematic liquid crystals. Preprint / Working Paper. University of Strathclyde, Glasgow.