Publications -- Matthew Hubbard

Refereed Journals

1. M.J.Baines, M.E.Hubbard and P.K.Jimack,
   Velocity-based moving mesh methods for nonlinear partial differential equations,
   Commun. Comput. Phys., 10(3):509--576, 2011. pdf
2. R.Marlow, M.E.Hubbard and P.K.Jimack,
   Moving mesh methods for solving parabolic partial differential equations,
   Comput. Fluids., 46(1):353--361, 2011. pdf
3. M.E.Hubbard and M.Ricchiuto,
   Discontinuous upwind residual distribution: A route to unconditional positivity and high order accuracy,
   Comput. Fluids., 46(1):263--269, 2011. pdf
4. M.E.Hubbard, P.M.Jones and B.D.Sleeman,
   The foundations of a unified approach to mathematical modelling of angiogenesis,
   Int. J. Adv. Eng. Sci. Appl. Math., 1:43--52, 2009. pdf
5. M.E.Hubbard, M.J.Baines and P.K.Jimack,
   Consistent Dirichlet boundary conditions for moving boundary problems,
   Appl. Numer. Math., 59(6):1337--1353, 2009. pdf
6. M.J.Baines, M.E.Hubbard, P.K.Jimack and R.Mahmood,
   A moving-mesh finite element method and its application to the numerical solution of phase-change problems,
   Commun. Comput. Phys., 6(3):595--624, 2009. pdf
7. M.E.Hubbard,
   Discontinuous fluctuation distribution,
   J. Comput. Phys., 227(24):10125--10147, 2008. pdf
8. M.E.Hubbard,
   A framework for discontinuous fluctuation distribution,
   Int. J. Numer. Methods Fluids, 56(8):1305--1311, 2008. pdf
9. M.E.Hubbard,
   Non-oscillatory third order fluctuation splitting schemes for steady scalar conservation laws,
   J. Comput. Phys., 222(2):740--768, 2007. pdf
10. M.J.Baines, M.E.Hubbard, P.K.Jimack and A.C.Jones,
    Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions,
    Appl. Numer. Math., 56:230--252, 2006. pdf
11. M.E.Hubbard, J.A.Leach and J.C.Wei,
    Pattern formation in a two-dimensional simple chemical system with general orders of autocatalysis and decay,
    IMA J. Appl. Math., 70(6):723--747, 2005. pdf
12. M.J.Baines, M.E.Hubbard and P.K.Jimack,
    A moving mesh finite element algorithm for fluid flow problems with moving boundaries,
    Int. J. Numer. Methods Fluids, 47(10/11):1077--1083, 2005. pdf
13. M.J.Baines, M.E.Hubbard and P.K.Jimack,
    A moving mesh finite element algorithm for the adaptive solution of time-dependent partial differential equations with moving boundaries,
    Appl. Numer. Math., 54:450--469, 2005. pdf
14. M.E.Hubbard and A.L.Laird,
    High order fluctuation splitting schemes for time-dependent advection on unstructured grids,
    Comput. Fluids, 34(4/5):443--459, 2005. pdf
15. M.E.Hubbard and N.Nikiforakis,
    A three-dimensional, adaptive, Godunov-type model for global atmospheric flows,
    Mon. Weather Rev., 131:1848--1864, 2003. pdf
16. M.E.Hubbard and N.Dodd,
    A 2d numerical model of wave run-up, overtopping and regeneration,
    Coastal Engineering, 47(1):1--26, 2002. pdf
17. M.E.Hubbard,
    Adaptive mesh refinement for three-dimensional off-line tracer advection over the sphere,
    Int. J. Numer. Methods Fluids, 40:369--377, 2002. pdf
18. M.J.Baines, S.J.Leary and M.E.Hubbard,
    Multidimensional least squares fluctuation distribution schemes with adaptive mesh movement for steady hyperbolic equations,
    SIAM J. Sci. Comput., 23(5):1485--1502, 2002. pdf (pictures missing)
19. M.E.Hubbard,
    On the accuracy of one dimensional models of steady converging/diverging open channel flows,
    Int. J. Numer. Methods Fluids, 35(7):785--808, 2001. pdf
20. M.E.Hubbard and P.Garcia-Navarro,
    Flux difference splitting and the balancing of source terms and flux gradients,
    J. Comput. Phys., 165(1):89--125, 2000. pdf (some odd-sized pictures)
21. M.E.Hubbard and P.L.Roe,
    Compact high resolution algorithms for time dependent advection on unstructured grids,
    Int. J. Numer. Methods Fluids, 33(5):711--736, 2000. pdf (abstract missing)
22. M.E.Hubbard,
    Multidimensional slope limiters for MUSCL-type finite volume schemes on unstructured grids,
    J. Comput. Phys., 155:54--74, 1999. pdf
23. M.E.Hubbard and M.J.Baines,
    Conservative multidimensional upwinding for the steady two dimensional shallow water equations,
    J. Comput. Phys., 138:419--448, 1997. pdf
24. P.Garcia-Navarro, M.E.Hubbard and A.Priestley,
    Genuinely multidimensional upwinding for the 2d shallow water equations,
    J. Comput. Phys., 121(1):79--93, 1995. pdf (pictures missing)

Conference Proceedings

1. M.E.Hubbard and M.Ricchiuto,
   Discontinuous residual distribution: A route to unconditional positivity and high order accuracy,
   in Proceedings of the 10th Conference on Numerical Methods for Fluid Dynamics, P.K.Sweby (Ed.), ICFD Reading, 2010. pdf
2. R.Marlow, M.E.Hubbard and P.K.Jimack,
   Moving mesh methods for solving parabolic PDEs,
   in Proceedings of the 10th Conference on Numerical Methods for Fluid Dynamics, P.K.Sweby (Ed.), ICFD Reading, 2010. pdf
3. M.E.Hubbard,
   Discontinuous fluctuation distribution for time-dependent problems,
   in Computational Fluid Dynamics 2008, H.Choi, H.G.Choi, J.Y.Yoo (Eds.), Springer-Verlag, pp. 711--716, 2009. pdf
4. M.E.Hubbard and N.Z.Mebrate,
   Very high order, non-oscillatory fluctuation distribution schemes,
   in Computational Fluid Dynamics 2006, H.Deconinck, E.Dick (Eds.), Springer-Verlag, pp. 65--70, 2009. pdf
5. M.E.Hubbard,
   A framework for discontinuous fluctuation distribution,
   in Proceedings of the 9th Conference on Numerical Methods for Fluid Dynamics, P.K.Sweby (Ed.), ICFD Reading, 2007. pdf
6. M.E.Hubbard,
   Non-oscillatory, third order fluctuation splitting schemes,
   in Finite Volumes for Complex Applications IV, F.Benkhaldoun, D.Ouazar, S.Raghay (Eds.), pp. 377--387, Hermes Science Publishing, 2005. pdf (pictures missing)
7. M.J.Baines, M.E.Hubbard and P.K.Jimack,
   A moving mesh finite element algorithm for fluid flow problems with moving boundaries,
   in Proceedings of the 8th Conference on Numerical Methods for Fluid Dynamics, M.J.Baines (Ed.), ICFD Oxford, 2004. pdf
8. M.J.Baines, M.E.Hubbard and P.K.Jimack,
   A Lagrangian moving finite element method incorporating monitor functions,
   in Advances in Scientific Computing and Applications, Y.Y.Lu, W.W.Sun, T.Tang (Eds.), Scientific Press, Beijing, pp. 32--44, 2004. pdf
9. M.J.Baines, M.E.Hubbard and P.K.Jimack,
   Adaptive finite element solutions of time-dependent partial differential equations using moving mesh algorithms,
   in "Modelling and Simulation in Chemical Engineering, Centro Internacional de Matematica 22", A.E.Rodrigues, P.de Oliveira, J.A.Castro, J.A.Ferreira (Eds.), Coimbra, Portugal, paper 3, 2003. pdf
10. M.E.Hubbard and M.Berzins,
    A positivity preserving finite element method for hyperbolic partial differential equations,
    in Computational Fluid Dynamics 2002, S.Armfield, P.Morgan, K.Srinivas (Eds.), Springer-Verlag, pp. 205-210, 2003. pdf
11. M.E.Hubbard,
    Adaptive mesh refinement for three-dimensional off-line tracer advection over the sphere,
    in Numerical Methods for Fluid Dynamics VII, M.J.Baines (Ed.), ICFD Oxford, pp. 355--361, 2001. pdf
12. M.E.Hubbard and P.Garcia-Navarro,
    Balancing source terms and flux gradients in finite volume schemes,
    in Godunov Methods: Theory and Applications, E.F.Toro (Ed.), Kluwer Academic/Plenum Publishers, pp. 477--483, 2001. pdf
13. P.Garcia-Navarro, P.Brufau and M.E.Hubbard,
    Upwinding in two dimensions,
    Invited Lecture in Godunov Methods: Theory and Applications, E.F.Toro (Ed.), Kluwer Academic/Plenum Publishers, pp. 343--365, 2001. pdf (some pictures missing)
14. M.E.Hubbard,
    Multidimensional upwind schemes for the shallow water equations,
    Invited Lecture in Numerical Simulation of Hydrodynamic Systems, pp. 131--154, 1999. pdf
15. M.J.Baines, S.J.Leary and M.E.Hubbard,
    A finite volume method for steady hyperbolic equations incorporating mesh movement,
    in Finite Volumes for Complex Applications -- Problems and Perspectives, R.Vilsmeier, F.Benkhaldoun, D.Hanel (Eds.), Hermes, pp. 787--794, 1999.
16. P.Sims, M.E.Hubbard and M.J.Baines,
    Multidimensional upwinding for the Euler equations,
    in International Workshop on New Models and Numerical Codes for Shock Wave Processes in Condensed Media, pp. 781--786, 1999.
17. M.J.Baines and M.E.Hubbard,
    Multidimensional upwinding with grid adaptation,
    in Numerical Methods for Wave Propagation, E.F.Toro, J.F.Clarke (Eds.), Kluwer Academic Publishers, pp. 33--54, 1998. pdf (pictures missing)
18. M.E.Hubbard and P.L.Roe,
    Multidimensional upwind fluctuation distribution schemes for time dependent problems,
    in Numerical Methods for Fluid Dynamics VI, M.J.Baines (Ed.), ICFD Oxford, pp. 363--369, 1998. pdf
19. M.E.Hubbard and M.J.Baines,
    Multidimensional upwinding and grid adaptation,
    in Numerical Methods for Fluid Dynamics V, K.W.Morton, M.J.Baines (Eds.), Oxford University Press, pp. 431--437, 1995. pdf (pictures missing)
20. P.Garcia-Navarro, M.E.Hubbard, A.Priestley and M.J.Baines,
    Two dimensional shallow water flows on unstructured grids,
    in Proceedings of 1st Asian CFD Conference, pp. 335--340, 1995. pdf (pictures missing)

Thesis

• M.E.Hubbard,
  Multidimensional upwinding and grid adaptation for conservation laws,
  Ph.D. thesis, The University of Reading, Department of Mathematics, 1996.

Internal Reports

• * 2003.04: M.J.Baines, M.E.Hubbard and P.K.Jimack,
  A moving finite element method using monitor functions, 2003. pdf

• NA--4/99: M.E.Hubbard,
  Aspects of multidimensional upwinding: time-dependent nonlinear systems, source terms, spherical geometries and three-dimensional grid adaptation, 1999. pdf (some pictures missing)
• * NA--3/99: M.E.Hubbard and P.Garcia-Navarro,
  Flux difference splitting and the balancing of source terms and flux gradients, 2000. pdf
• * NA--1/99: M.E.Hubbard,
  On the accuracy of one dimensional models of steady converging/diverging open channel flows, 1999. pdf
• * NA--8/98: M.E.Hubbard,
  Multidimensional slope limiters for MUSCL-type finite volume schemes II - on improving existing unstructured grid techniques, 1998. pdf
• NA--2/98: M.E.Hubbard,
  Multidimensional slope limiters for MUSCL-type finite volume schemes, 1998. pdf
• * NA--1/98: M.E.Hubbard and P.L.Roe,
  Multidimensional upwind fluctuation distribution schemes for scalar time-dependent problems, 1998. pdf
• NA--6/97: M.E.Hubbard,
  Least squares minimisation and steepest descent methods for the scalar advection equation and a Cauchy-Riemann system on an adaptive grid, 1997. pdf
• * NA--1/97: M.E.Hubbard and M.J.Baines,
  Conservative multidimensional upwinding for the steady two dimensional shallow water equations, 1997. pdf
• NA--4/95: M.E.Hubbard, P.Garcia-Navarro and M.J.Baines,
  Conservative multidimensional upwinding for the shallow water equations, 1995. pdf (pictures and references missing)
• NA--8/94: M.E.Hubbard,
  Grid adaptation and multidimensional upwinding, 1994. pdf
• * NA--3/94: P.Garcia-Navarro, M.E.Hubbard and A.Priestley,
  Genuinely multidimensional upwinding for the 2d shallow water equations, 1994. pdf (pictures missing)
• NA--7/93: M.E.Hubbard,
  A survey of genuinely multi-dimensional upwinding techniques, 1993. pdf
• NA--2/93: M.E.Hubbard,
  A hybrid central/upwind approach to the solution of the one dimensional Euler equations, 1993. pdf

Manuals

• M.E.Hubbard and N.Dodd,
  ANEMONE: OTT-2D, A user manual (version 1),
  Report TR-65, HR Wallingford Ltd., 2000.
• M.E.Hubbard and N.Dodd,
  ANEMONE: LFW-2D, A user manual (version 1),
  Report TR-86, HR Wallingford Ltd., 2000.
• M.E.Hubbard,
  AMR3D: a user's guide,
  DAMTP, 2001.

Possibly on the horizon...

• M.E.Hubbard and M.Ricchiuto, Second order space-time residual distribution: discontinuous temporal and/or spatial approximations.
• M.E.Hubbard,
  Data structures for visualising structured AMR data. pdf (full draft, started in 2000)
• M.E.Hubbard and N.Z.Mebrate,
  A positive, high order fluctuation splitting scheme based on extending the stencil.
• M.E.Hubbard,
  Fluctuation splitting on the sphere.
• M.E.Hubbard,
  Positive, high order fluctuation splitting for time-dependent conservation laws.
• M.E.Hubbard,
  A geometric view of the PSI scheme. pdf (unfinished and dates from 1995)