School of Mathematics, Statistics & Actuarial Science

About

Professor Mansfield is a member of the School's Promotions Committee.

She is a Vice-President of the Institute of Mathematics and its Applications (IMA), with responsibility for Learned Societies, and Chair of the IMA Research Committee.

Additional professional affiliations and service:

Contact Information

Address

Room 245

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Publications

Also view these in the Kent Academic Repository

Article
Beffa, G. and Mansfield, E. (2016). Discrete moving frames on lattice varieties and lattice based multispace. Foundations of Computational Mathematics [Online]. Available at: http://dx.doi.org/10.1007/s10208-016-9337-5.
Mansfield, E. and Goncalves, T. (2016). Moving Frames and Noether's Conservation Laws – the General Case. Forum of Mathematics, Sigma [Online]. Available at: https://www.cambridge.org/core/journals/forum-of-mathematics-sigma/article/moving-frames-and-noethers-conservation-lawsthe-general-case/EC6B14C57AFE3EEE95A18969B6B5.
Mansfield, E. and Pryer, T. (2014). Noether type discrete conserved quantities arising from a finite element approximation of a variational problem. Foundations of Computational Mathematics [Online]:1-34. Available at: http://dx.doi.org/10.1007/s10208-015-9298-0.
Goncalves, T. and Mansfield, E. (2013). Moving Frames and Conservation Laws for Euclidean Invariant Lagrangians. Studies in Applied Mathematics [Online] 130:134-166. Available at: http://dx.doi.org/10.1111/j.1467-9590.2012.00566.x.
Mansfield, E., Marí Beffa, G. and Wang, J. (2013). Discrete Moving Frames and Discrete Integrable Systems. Foundations of Computational Mathematics [Online] 13:545-582. Available at: http://dx.doi.org/10.1007/s10208-013-9153-0.
Mansfield, E. and Goncalves, T. (2011). On Moving Frames and Noether's Conservation Laws. Studies in Applied Mathematics [Online] 128:1-29. Available at: http://dx.doi.org/10.1111/j.1467-9590.2011.00522.x.
Hydon, P. and Mansfield, E. (2011). Extensions of Noether's Second Theorem: from continuous to discrete systems. Proceedings of the Royal Society A- Mathematical Physical and Engineering Sciences [Online] 467:3206-3221. Available at: http://dx.doi.org/10.1098/rspa.2011.0158.
Mansfield, E. and Hydon, P. (2008). Difference forms. Foundations of Computational Mathematics [Online] 8:427-467. Available at: http://dx.doi.org/10.1007/s10208-007-9015-8.
Mansfield, E. and van der Kamp, P. (2006). Evolution of curvature invariants and lifting integrability. Journal of Geometry and Physics [Online] 56:1294-1325. Available at: http://dx.doi.org/10.1016/j.geomphys.2005.07.002.
Bila, N., Mansfield, E. and Clarkson, P. (2006). Symmetry group analysis of the shallow water and semi-geostrophic equations. Quarterly Journal of Mechanics and Applied Mathematics [Online] 59:95-123. Available at: http://dx.doi.org/10.1093/qjmam/hbi033.
Mansfield, E. (2006). Noether's Theorem for Smooth, Difference and Finite Element Schemes. Foundations of Computational Mathematics, Santander 2005 [Online] London:230-254. Available at: http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521681612.
Mansfield, E. and Quispel, R. (2005). Towards a variational complex for the finite element method. Group Theory and Numerical Analysis 39:207-232.
Hydon, P. and Mansfield, E. (2004). A variational complex for difference equations. Foundations of Computational Mathematics 4:187-217.
Mansfield, E. and Szanto, A. (2003). Elimination Theory for differential difference polynomials. Proceedings of the 2003 International Symposium for Symbolic Algebra and Computation [Online]:191-198. Available at: http://doi.acm.org/10.1145/860854.860897.
Clarkson, P. and Mansfield, E. (2003). The second Painleve equation, its hierarchy and associated special polynomials. Nonlinearity [Online] 16:R1-R26. Available at: http://dx.doi.org/10.1088/0951-7715/16/3/201.
Mansfield, E. (2001). Algorithms for symmetric differential systems. Foundations of Computational Mathematics 1:335-383.
Mansfield, E. and Hydon, P. (2001). On a variational complex for difference equations. Contemporary Mathematics 285:195-205.
Mansfield, E. (1999). The nonclassical group analysis of the heat equation. Journal of Mathematical Analysis and Applications [Online] 231:526-542. Available at: http://dx.doi.org/10.1006/jmaa.1998.6250.
Mansfield, E., Reid, G. and Clarkson, P. (1998). Nonclassical reductions of a 3+1-cubic nonlinear Schrodinger system. Computer Physics Communications [Online] 115:460-488. Available at: http://dx.doi.org/10.1016/S0010-4655(98)00136-2.
Mansfield, E. and Webster, H. (1998). On one-parameter families of Painleve III. Studies in Applied Mathematics [Online] 101:321-341. Available at: http://dx.doi.org/10.1111/1467-9590.00096.
Clarkson, P., Mansfield, E. and Priestley, T. (1997). Symmetries of a class of nonlinear third-order partial differential equations. Mathematical and Computer Modelling 25:195-212.
Mansfield, E. and Clarkson, P. (1997). Symmetries and exact solutions for a 2+1-dimensional shallow water wave equation. Mathematics and Computers in Simulation [Online] 43:39-55. Available at: http://dx.doi.org/10.1016/S0378-4754(96)00054-7.
Mansfield, E. and Clarkson, P. (1997). Applications of the differential algebra package diffgrob2 to classical symmetries of differential equations. Journal of Symbolic Computation [Online] 23:517-533. Available at: http://dx.doi.org/10.1006/jsco.1996.0105.
Albrecht, D., Mansfield, E. and Milne, A. (1996). Algorithms for special integrals of ordinary differential equations. Journal of Physics A: Mathematical and General [Online] 29:973-991. Available at: http://dx.doi.org/10.1088/0305-4470/29/5/013.
Mansfield, E. (1996). A simple criterion for involutivity. Journal of the London Mathematical Society [Online] 54:323-345. Available at: http://dx.doi.org/10.1112/jlms/54.2.323.
Clarkson, P., Mansfield, E. and Milne, A. (1996). Symmetries and exact solutions of a (2+1)-dimensional sine-Gordon system. Philosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences. [Online] 354:1807-1835. Available at: http://dx.doi.org/10.1098/rsta.1996.0079.
Mansfield, E. (1996). The differential algebra package diffgrob2. Mapletech 3:33-37.
Clarkson, P., Mansfield, E. and Milne, A. (1996). Symmetries and exact solutions of a 2+1 dimensional sine-Gordon equation. Philosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences. 354:1807-1835.
Book section
Mansfield, E. and Zhao, J. (2011). On the modern notion of a moving frame. in: Dorst, L. and Lasenby, J. eds. Guide to Geometric Algebra in Practice. London: Springer, pp. 411-434. Available at: http://dx.doi.org/10.1007/978-0-85729-811-9_20.
Clarkson, P., Mansfield, E. and Webster, H. (2002). On Discrete Painleve Equations as Backlund Transformations. in: Coley, A. et al. eds. Backlund and Darboux Transformations: The Geometry of Solitons. United States: American Mathematical Society, pp. 129-139.
Clarkson, P. and Mansfield, E. (2002). Open problems in symmetry analysis. in: Leslie, J. ed. The Geometrical Study of Differential Equations. United Kingdom: American Mathematical Society, pp. 195-205.
Mansfield, E. (2002). Moving frames and differential algebra. in: Guo, L. et al. eds. Differential Algebra and Related Topics. Singapore: World Scientific Press, pp. 257-279. Available at: http://www.worldscibooks.com/mathematics/4768.html.
Conference or workshop item
Shemyakova, E. and Mansfield, E. (2008). Moving Frames for Laplace Invariants. in: Jeffrey, D. ed. International Symposium in Symbolic and Algebraic Manipulation 2008. New York: Association for Computing Machinery, pp. 291-298. Available at: http://portal.acm.org/toc.cfm?id=1390768&coll=ACM&dl=ACM&type=proceeding&idx=SERIES418&part=series&WantType=Proceedings&title=ISSAC&CFID=://www.google.co.uk/search?q=ISSAC%2001%20Proceedings%20&CFTOKEN=www.google.co.uk/search?q=ISSAC%2001%20Proceedings.
Mansfield, E. and Hydon, P. (2001). Towards approximations which preserve integrals. in: Mourrain, B. ed. International Symposium in Symbolic and Algebraic Manipulation. New York: Association for Computing Machinery, pp. 217-222. Available at: http://portal.acm.org/toc.cfm?id=384101&coll=ACM&dl=ACM&type=proceeding&idx=SERIES418&part=series&WantType=Proceedings&title=International+Conference+on+Symbolic+and+Algebraic+Computation.
Clarkson, P., Mansfield, E. and Webster, H. (2000). On the relation between the continuous and discrete Painleve equations. in: 12th International Workshop on Nonlinear Evolution Equations and Dynamical Systems (NEEDS 98). Springer Science and Business Media, pp. 1-16. Available at: http:di.dox.org/10.1007/BF02551165.
Book
Mansfield, E. (2010). A Practical Guide to the Invariant Calculus. Cambridge: Cambridge University Press.
Total publications in KAR: 36 [See all in KAR]
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Research Interests

  • Discrete variational methods, with applications to geometric integration
  • Noether’s Theorem in all its manifestations
  • Moving frames, discrete moving frames
  • Multispace methods
  • Symbolic analysis for nonlinear differential and difference equations.
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Teaching

MA561/MA603: Introduction to Lie Groups and Algebras back to top

Research Supervisees

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School of Mathematics, Statistics and Actuarial Science (SMSAS), Sibson Building, Parkwood Road, Canterbury, CT2 7FS

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Last Updated: 07/09/2018