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Prof Mark A Kelmanson

Professor of Applied Mathematics
Applied Mathematics

Contact details

Room: Satellite 10.07
Tel: +44 (0)113 3435150
Email: M.Kelmanson @


Thin-film fluid mechanics
Coating flows
Ophthalmic flows
Multiple timescales
Algebraic manipulators
Fredholm integral equations
Error analysis

Research interests

As a member of the Polymers and Industrial Mathematics (PIM) group, my main current research interests are in the field of thin-fim viscous fluid mechanics, with particular emphasis on the development of (possibly automated) asymptotic methods for both deriving and solving the spatio-temporal evolution equations arising in both industrial coating flows and ophthalmic flows.

Other industrially related research has been done under funded collaborations with: Dr Daniel Read (Maths, PIM) on computational linear rheology; Professor Peter Jimack (Computing) on fully adaptive finite-element methods for free-surface viscous flows; PPG Protective and Marine Coatings (industrial sponsors) on the modelling of fire-resistant properties of reactive intumescent protective coatings, and; Defence Research Agency (Fort Halstead) on the modelling of high-velocity impact phenomena.

As a former member of the now-disbanded Computational PDEs group, my other current research interests involve error analyses of numerical methods for solving Fredholm integral equations of the second kind, because many examples of these arise when modelling industrial problems. A full understanding of the errors incurred in such methods may enable improved techniques to be developed and implemented. For example, recent research on problems involving boundary singularities can provide an better insight into crack formation in elastostatics.

Useful links

Personal homepage
PIM group page
Industrial placement page

Postgraduate students

Abigail Fairbairn (2014)
Claire McIlroy (2011)
Tomasz Salwa (2014)

Selected publications

Groh, C.M. and Kelmanson, M.A., Computer-algebra multiple-timescale method for spatially periodic thin-film viscous-flow problems, Int. J. Num. Meth. Fluids, to appear, (published online as doi: 10.1002/fld.2458).

Kelmanson, M.A. and Tenwick, M.C., Error reduction in Gauss-Jacobi Nyström quadrature for Fredholm integral equations of the second kind, CMES, 55(2),191-210, 2010.

Groh, C.M. and Kelmanson, M.A., Multiple-timescale asymptotic analysis of transient coating flows, Phys. Fluids, 21(9), 091702, 2009.

Kelmanson, M.A., On inertial effects in the Moffatt-Pukhnachov coating-flow problem, J. Fluid Mech., 633, 327-354, 2009.