Imperial College London


Faculty of Natural SciencesDepartment of Mathematics

Professor of Computational Mathematics



+44 (0)20 7594 3468colin.cotter




755Huxley BuildingSouth Kensington Campus





My research in numerical analysis and scientific computing focusses on the design, analysis and implementation of numerical methods for weather forecasting, ocean modelling and climate simulation. Recently, I have been developing compatible finite element methods and time parallel algorithms for these applications. I am motivated by the geometric variational structure of fluid equations, which are also relevant for algorithms for exploring the geometric structure of shapes and images. I also develop numerical algorithms for probabilistic forecasting and data assimilation, and am currently developing particle filters for stochastic partial differential equations.

I am co-Director for the Mathematics of Planet Earth Centre for Doctoral Training, and a co-Investigator for the Platform for Research in Simulation Methods. I am also an Associate Editor for Foundations of Data Science (was previously Associate Editor for for the Quarterly Journal of the Royal Meteorological Society) and am a member of the EPSRC peer review college. I wrote a book with Sebastian Reich, entitled "Probabilistic Forecasting and Bayesian Data Assimliation".

See my research page for the list of current and past PhD and postdoctoral researchers.


  • Professor of Computational Mathematics, Department of Mathematics, Imperial College London, July 2019 - date
  • Reader in Numerical Analysis and Scientific Computing, Department of Mathematics, Imperial College London, July 2016 - July 2019
  • Senior Lecturer in the Department of Mathematics, Imperial College London, November 2013 to July 2016
  • Senior Lecturer in the Department of Aeronautics, Imperial College London 2010-2013
  • Lecturer in the Department of Aeronautics, Imperial College London 2006-2010
  • Postdoctoral researcher in the Department of Mathematics, Imperial College London 2005-2006
  • Postdoctoral researcher in the Department of Earth Science and Engineering, Imperial College London 2004-2005
  • PhD Mathematics, Imperial College London 2000-2004
  • Part III, Mathematics, Fitzwilliam College, Cambridge University 1999-2000
  • BA Mathematics, Fitzwilliam College, Cambridge University 1996-1999

    My Google Scholar profile is here. Preprints of many of my papers can be found here.

    Selected Publications

    Journal Articles

    Cotter CJ, Deasy J, Pryer T, 2020, The r-Hunter-Saxton equation, smooth and singular solutions and their approximation, Nonlinearity, Vol:33, ISSN:0951-7715, Pages:7016-7039

    Wimmer GA, Cotter CJ, Bauer W, 2020, Energy conserving upwinded compatible finite element schemes for the rotating shallow water equations, Journal of Computational Physics, Vol:401, ISSN:0021-9991, Pages:1-18

    Cotter CJ, Crisan D, Holm DD, et al., 2019, Numerically modelling stochastic lie transport in fluid dynamics, SIAM Journal on Scientific Computing, Vol:17, ISSN:1064-8275, Pages:192-232

    Cotter CJ, Graber PJ, Kirby RC, 2018, Mixed finite elements for global tide models with nonlinear damping, Numerische Mathematik, Vol:140, ISSN:0029-599X, Pages:963-991

    Gregory ACA, Cotter CJ, 2017, A seamless multilevel ensemble transform particle filter, Siam Journal on Scientific Computing, Vol:39, ISSN:1095-7197, Pages:A2684-A2701

    Cotter CJ, Gottwald G, Holm DD, 2017, Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics, Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences, Vol:473, ISSN:1364-5021

    Natale A, Cotter CJ, 2017, A variational H (div) finite-element discretization approach for perfect incompressible fluids, IMA Journal of Numerical Analysis, Vol:38, ISSN:0272-4979, Pages:1388-1419

    Natale A, Shipton J, Cotter CJ, 2016, Compatible finite element spaces for geophysical fluid dynamics, Dynamics and Statistics of the Climate System, Vol:1, ISSN:2059-6987

    Cotter CJ, Thuburn J, 2014, A finite element exterior calculus framework for the rotating shallow-water equations, Journal of Computational Physics, Vol:257, Pages:1506-1526

    Cotter CJ, Shipton J, 2012, Mixed finite elements for numerical weather prediction, J. Comp. Phys.


    Reich S, Cotter CJ, 2015, Probabilistic Forecasting and Bayesian Data Assimilation,, Cambridge University Press, ISBN:9781107663916

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