Baines, M. J. and Christou, K. (2022) A numerical method for multispecies populations in a moving domain using combined masses. Mathematics, 10 (7). e1124. ISSN 2227-7390 doi: https://doi.org/10.3390/math10071124

Baines, M. J. and Christou, K. (2021) A moving-mesh finite-difference method for segregated two-phase competition-diffusion. Mathematics, 9 (4). 386. ISSN 2227-7390 doi: https://doi.org/10.3390/math9040386

Lukyanov, A., Mitkin, V., Theofanous, T. G. and Baines, M. (2019) Capillary transport in particulate porous media at low levels of saturation. Journal of Applied Physics, 125. 185301. ISSN 0021-8979 doi: https://doi.org/10.1063/1.5086869

Baines, M. J. and Sarahs, N. (2018) A moving-mesh finite difference scheme that preserves scaling symmetry for a class of nonlinear diffusion problems. Journal of Computational and Applied Mathematics, 340. pp. 380-389. ISSN 0377-0427 doi: https://doi.org/10.1016/j.cam.2018.02.040

Bonan, B., Nichols, N. K. ORCID: https://orcid.org/0000-0003-1133-5220, Baines, M. J. and Partridge, D. (2017) Data assimilation for moving mesh methods with an application to ice sheet modelling. Nonlinear Processes in Geophysics, 24 (3). pp. 515-534. ISSN 1023-5809 doi: https://doi.org/10.5194/npg-24-515-2017

Bonan, B., Baines, M., Nichols, N. ORCID: https://orcid.org/0000-0003-1133-5220 and Partridge, D. (2016) A moving-point approach to model shallow ice sheets: a study case with radially symmetrical ice sheets. The Cryosphere, 10 (1). pp. 1-14. ISSN 1994-0424 doi: https://doi.org/10.5194/tc-10-1-2016

Lee, T. E., Baines, M. J. and Langdon, S. (2015) A finite difference moving mesh method based on conservation for moving boundary problems. Journal of Computational and Applied Mathematics, 288. pp. 1-17. ISSN 0377-0427 doi: https://doi.org/10.1016/j.cam.2015.03.032

Bonan, B., Baines, M. J., Nichols, N. K. ORCID: https://orcid.org/0000-0003-1133-5220 and Partridge, D. (2015) A moving point approach to model shallow ice sheets: a study case with radially-symmetrical ice sheets. The Cryosphere Discussions, 9 (4). pp. 4237-4270. ISSN 1994-0432 doi: https://doi.org/10.5194/tcd-9-4237-2015

Baines, M. J. (2015) Explicit time-stepping for moving meshes. Journal of Mathematical Study, 48 (2). pp. 93-105. ISSN 1006-6837 doi: https://doi.org/10.4208/jms.v48n2.15.01

Baines, M. J. and Lee, T. E. (2014) A large time-step implicit moving mesh scheme for moving boundary problems. Numerical Methods for Partial Differential Equations, 30 (1). pp. 321-338. ISSN 1098-2426 doi: https://doi.org/10.1002/num.21812

Lee, T. E., Baines, M. J., Langdon, S. and Tindall, M. J. (2013) A moving mesh approach for modelling avascular tumour growth. Applied Numerical Mathematics, 72. pp. 99-114. ISSN 01689274 doi: https://doi.org/10.1016/j.apnum.2013.06.001

Lukyanov, A. V., Shushchikh, M. M., Baines, M. J. and Thoephanus, T. G. (2012) Superfast nonlinear diffusion: capillary transport in particulate porous media. Physical Review Letters, 109 (21). pp. 214501-214504. ISSN 0031-9007 doi: https://doi.org/10.1103/PhysRevLett.109.214501

Lukyanov, A.V., Sushchikh, M.M., Baines, M.J. and Theofanous, T.G. (2012) Superfast non-linear diffusion: capillary transport in particulate porous media. Physical Review Letters, 109 (21). 214501. ISSN 0031-9007 doi: https://doi.org/10.1103/PhysRevLett.109.214501

Baines, M. J., Hubbard, M. E. and Jimack, P. K. (2011) Velocity-based moving mesh methods for nonlinear partial differential equations. Communications in Computational Physics, 10 (3). pp. 509-576. ISSN 1991-7120 doi: https://doi.org/10.4208/cicp.201010.040511a

Baines, M. J. and Partridge, D. (2011) A moving mesh approach to an ice sheet model. Computers and Fluids, 46 . pp. 381-386. ISSN 0045-7930 doi: https://doi.org/10.1016/j.compfluid.2011.02.001

Dance, S. L. ORCID: https://orcid.org/0000-0003-1690-3338, Baines, M. J., Lawless, A. S. ORCID: https://orcid.org/0000-0002-3016-6568, Mason, D. C. ORCID: https://orcid.org/0000-0001-6092-6081, Nichols, N. K. ORCID: https://orcid.org/0000-0003-1133-5220, Scott, T. R., Sweby, P. K. ORCID: https://orcid.org/0009-0003-8488-0251, Smith, P. and Thornhill, G. D. (2010) Use of data assimilation methods in coastal sediment models. In: Flood Risk from Extreme Events (FREE) Final Science Meeting, 20 October, London. (Unpublished)

Thornhill, G. D., Scott, T. R., Dance, S. L. ORCID: https://orcid.org/0000-0003-1690-3338, Mason, D. C. ORCID: https://orcid.org/0000-0001-6092-6081, Nichols, N. K. ORCID: https://orcid.org/0000-0003-1133-5220, Baines, M. J., Horsburgh, K. and Sweby, P. K. ORCID: https://orcid.org/0009-0003-8488-0251 (2010) Data assimilation and morphodynamic modelling of Morecambe Bay. In: National Centre for Earth Observation Annual Conference, 28-30 September 2010, Leicester. (Unpublished)

Smith, P. ORCID: https://orcid.org/0000-0003-4570-4127, Dance, S. L. ORCID: https://orcid.org/0000-0003-1690-3338, Baines, M. J., Nichols, N. K. ORCID: https://orcid.org/0000-0003-1133-5220 and Scott, T. R. (2009) Variational data assimilation for parameter estimation: application to a simple morphodynamic model. Ocean Dynamics, 59 (5). pp. 697-708. ISSN 1616-7341 doi: https://doi.org/10.1007/s10236-009-0205-6

Hubbard, M. E., Baines, M. J. and Jimack, P. K. (2009) Consistent Dirichlet Boundary Conditions for Numerical Solution of Moving Boundary Problems. Applied Numerical Mathematics, 59 (6). 1337-1353 . ISSN 0168-9274 doi: https://doi.org/10.1016/j.apnum.2008.08.002

Smith, P. J. ORCID: https://orcid.org/0000-0003-4570-4127, Dance, S. L. ORCID: https://orcid.org/0000-0003-1690-3338, Baines, M. J., Nichols, N. K. ORCID: https://orcid.org/0000-0003-1133-5220 and Scott, T. R. (2009) Variational data assimilation for morphodynamic model parameter estimation. In: Centre for Australian Weather and Climate Research (CAWCR) Workshop on Ensemble Prediction and Data Assimilation, February 2009, Australian Bureau of Meteorology, Melbourne.

Thornhill, G. D., Scott, T. R., Smith, P.J., Dance, S. L. ORCID: https://orcid.org/0000-0003-1690-3338, Mason, D. C. ORCID: https://orcid.org/0000-0001-6092-6081, Nichols, N. K. ORCID: https://orcid.org/0000-0003-1133-5220, Baines, M. J., Horsburgh, K.J., Sweby, P. K. ORCID: https://orcid.org/0009-0003-8488-0251 and Lawless, A. S. ORCID: https://orcid.org/0000-0002-3016-6568 (2009) Progress on “Changing coastlines: data assimilation for morphodynamic prediction and predictability”. In: Third NERC FREE Conference, 10-11 September, Plymouth. (Unpublished)

Smith, P. J., Dance, S. L. ORCID: https://orcid.org/0000-0003-1690-3338, Baines, M. J., Nichols, N. K. ORCID: https://orcid.org/0000-0003-1133-5220 and Scott, T. R. (2009) Variational data assimilation for morphodynamic model parameter estimation. In: The 8th International Workshop on Adjoint Model Applications in Dynamic Meteorology, May 2009, Tannersville, PA, USA.

Hubbard, M.E., Baines, M., Jimack, P.K. and Mahmood, R. (2009) A moving-mesh finite element method and its application to the numerical solution of phase-change problems. Communications in Computational Physics, 6 (3). pp. 595-624. ISSN 1815-2406

Scott, T. R., Smith, P. J. ORCID: https://orcid.org/0000-0003-4570-4127, Dance, S. L. ORCID: https://orcid.org/0000-0003-1690-3338, Mason, D.C. ORCID: https://orcid.org/0000-0001-6092-6081, Baines, M.J., Nichols, N.K. ORCID: https://orcid.org/0000-0003-1133-5220, Horsburgh, K.J., Sweby, P.K. ORCID: https://orcid.org/0009-0003-8488-0251 and Lawless, A.S. ORCID: https://orcid.org/0000-0002-3016-6568 (2008) Data assimilation for morphodynamic prediction and predictability. In: Coastal Engineering 2008 Proceedings of the 31st International Conference. World Scientific, pp. 2386-2398. doi: https://doi.org/10.1142/9789814277426_0197

Scott, T. R., Smith, P. J. ORCID: https://orcid.org/0000-0003-4570-4127, Dance, S.L. ORCID: https://orcid.org/0000-0003-1690-3338, Mason, D.C. ORCID: https://orcid.org/0000-0001-6092-6081, Nichols, N.K. ORCID: https://orcid.org/0000-0003-1133-5220, Baines, M.J., Horsburgh, K., Sweby, P. K. ORCID: https://orcid.org/0009-0003-8488-0251 and Lawless, A.S. ORCID: https://orcid.org/0000-0002-3016-6568 (2007) Progress on Changing coastlines: data assimilation for morphodynamic prediction and predictability. In: 2nd NERC Conference on Flood Risk from Extreme Events (FREE). (Unpublished)

Baines, M. J., Hubbard, M. E., Jimack, P. K. and Jones, A. C. (2006) Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions. Applied Numerical Mathematics, 56 (2). pp. 230-252. ISSN 0168-9274

Sun, K.H., Pyle, D.L., Baines, M.J., Hall-Taylor, N. and Fitt, A.D. (2006) Velocity profiles and frictional pressure drop for shear thinning materials in lid-driven cavities with fully developed axial flow. Chemical Engineering Science, 61 (14). pp. 4697-4706. ISSN 0009-2509 doi: https://doi.org/10.1016/j.ces.2006.03.005

Wells, B. V., Baines, M. J. and Glaister, P. (2005) Generation of arbitrary Lagrangian-Eulerian (ALE) velocities, based on monitor functions, for the solution of compressible fluid equations. International Journal for Numerical Methods in Fluids, 47 (10-11). pp. 1375-1381. ISSN 0271-2091

Baines, M. J., Hubbard, M. E. and Jimack, P. K. (2005) A moving mesh finite element algorithm for fluid flow problems with moving boundaries. International Journal for Numerical Methods in Fluids, 47 (10-11). pp. 1077-1083. ISSN 0271-2091

Baines, M. J., Hubbard, M. E. and Jimack, P. K. (2005) A moving mesh finite element algorithm for the adaptive solution of time-dependent partial differential equations with moving boundaries. Applied Numerical Mathematics, 54 (3-4). pp. 450-469. ISSN 0168-9274

Glaister, P., Baines, M. J. and Wells, B. V. (2004) Generation of Arbitrary Lagrangian-Eulerian (ALE) velocities, based on monitor functions, for the solution of compressible fluid equations. In: 8th International ICFD Conference on Numerical Methods for Fluid Dynamics, 29 Mar-1st Apr, Oxford.

Glaister, P., Baines, M. J. and Wells, B. V. (2004) An Arbitrary Lagrangian-Eulerian (ALE) method based on monitor functions for the compressible flow equations. In: SIAM Annual Meeting, Oregon.

Wakefield, M. A., Baines, M. J. and Porter, D. (2004) Bounds on physical quantities of interest via degenerate saddle-shaped functionals. Computers & Fluids, 33 (5-6). pp. 881-888. ISSN 0045-7930

Baines, M. J. and Sweby, P.K., eds. (2004) Numerical Methods for Fluid Dynamics VIII. Proceedings of Conference on Numerical Methods for Fluid Dynamics. ICFD, Oxford.

Sun, K.H., Pyle, D.L., Fitt, A.D., Please, C.P., Baines, M. J. and Hall-Taylor, N. (2004) Numerical study of 2D heat transfer in a scraped surface heat exchanger. Computers & Fluids, 33 (5-6). pp. 869-880. ISSN 0045-7930 doi: https://doi.org/10.1016/j.compfluid.2003.06.009

Lemos, A. C., Baines, M. J. and Nichols, N. K. ORCID: https://orcid.org/0000-0003-1133-5220 (2004) Upwind solution of singular differential equations arising from steady channel flows. Computers & Fluids, 33 (5-6). pp. 821-827. ISSN 0045-7930 doi: https://doi.org/10.1016/j.compfluid.2003.06.004

Wakefield, M.A., Baines, M. J. and Porter, D. (2003) Bounds on physical quantities. Computers & Fluids, 33. pp. 881-888. ISSN 0045-7930

Baines, M. J., Hubbard, M.E. and Jimack, P.K. (2003) A Lagrangian Moving Finite Element Method incorporating Monitor Functions. In: Advances in Scientific Computing and Applications. Proceedings of the 3rd Workshop on Numerical Methods for Partial Differential Equations., Hong Kong.

Baines, M. J. (2002) Moving meshes, conservation laws and least squares equidistribution. International Journal of Numerical Methods for Fluids, 40 (1-2). pp. 3-19. ISSN 1097-0363 doi: https://doi.org/10.1002/fld.294

Johnson, T. C., Baines, M. J. and Sweby, P. K. ORCID: https://orcid.org/0009-0003-8488-0251 (2002) A box scheme for transcritical flow. International Journal for Numerical Methods in Engineering, 55 (8). pp. 895-912. ISSN 1097-0207 doi: https://doi.org/10.1002/nme.525

Baines, M. J., Leary, S. J. and Hubbard, M. E. (2002) Multidimensional least squares fluctuation distribution schemes with adaptive mesh movement for steady hyperbolic equations. SIAM Journal on Scientific Computing, 23 (5). pp. 1485-1502. ISSN 1095-7197 doi: https://doi.org/10.1137/S1064827500370202

Miller, K. and Baines, M. J. (2001) Least squares moving finite elements. IMA Journal of Numerical Analysis, 21 (3). pp. 621-642. ISSN 1464-3642 doi: https://doi.org/10.1093/imanum/21.3.621

Baines, M. J. (2001) The solution of steady PDEs on adjustable meshes in multidimensions using local descent methods. In: Vande Wouwer, A., Saucez, P. and Schlesser, W. (eds.) Adaptive Method of Lines. Chapman & Hall, New York. ISBN 9781584882312

Baines, M.J. (2001) Moving finite element, least squares, and finite volume approximations of steady and time-dependent PDEs in multidimensions. Journal of Computational and Applied Mathematics, 128 (1-2). pp. 363-381. ISSN 1879-1778 doi: https://doi.org/10.1016/S0377-0427(00)00519-7

MacDonald, I., Baines, M., Nichols, N. ORCID: https://orcid.org/0000-0003-1133-5220 and Samuels, P. G. (1997) Analytic Benchmark Solutions for Open-Channel Flows. Journal of Hydraulic Engineering, 123 (11). p. 1041. ISSN 0733-9429 doi: https://doi.org/10.1061/(ASCE)0733-9429(1997)123:11(1041)

MacDonald, I., Baines, M. J., Nichols, N. ORCID: https://orcid.org/0000-0003-1133-5220 and Samuels, P. G. (1995) A new method for the computation of steady open channel trans-critical flow. In: The XXVIth Congress of the International Association for Hydyraulic Research, London.

Neylon, K. J., Baines, M. J. and Nichols, N. ORCID: https://orcid.org/0000-0003-1133-5220 (1994) Bi-CGSTAB for advection dominated problems. In: Lewis, J. G. (ed.) Proc. of the Fifth SIAM Conference on Applied Linear Algebra. SIAM, pp. 439-443.