## Publications

- O.M. Matsiaka, C.J. Penington, R.E. Baker and
**M.J. Simpson**(2018). Discrete and continuum approximations for collective cell migration in a scratch assay with cell size dynamics. - D.J. Warne, R.E. Baker and
**M.J. Simpson**(2018). Multilevel rejection sampling for approximate Bayesian computation. - E.J. Carr and
**M.J. Simpson**(2018). Accurate and efficient calculation of finite response times for groundwater flow . To appear, Journal of Hydrology. **M.J. Simpson**(2018). Calculating groundwater response times for flow in heterogeneous porous media . Groundwater. DOI: 10.1111/gwat.12587- A.P. Browning, S.W. McCue, R.N. Binny, M.J. Plank, E.T. Shah and
**M.J. Simpson**(2018). Inferring parameters for a lattice-free model of cell migration and proliferation using experimental data. Journal of Theoretical Biology. 437: 251-260. - D.J. Warne, R.E. Baker and
**M.J. Simpson**(2017). Optimal quantification of contact inhibition in cell populations . Biophysical Journal (Biophysical Letter). 113: 1920-1924. **M.J. Simpson**and M.J. Plank (2017). Simplified calculation of diffusivity for a lattice-based random walk with a single obstacle. Results in Physics. 7: 3346-3348.**M.J. Simpson**, S. McInerney, E.J. Carr and L. Cuttle (2017). Quantifying the efficacy of first aid treatments for burn injuries using mathematical modelling and in vivo porcine experiments. Scientific Reports. 7: 10925- P. Haridas, J.A. McGovern, D.L.S. McElwain and
**M.J. Simpson**(2017). Quantitative comparison of the spreading and invasion of radial growth phase and metastatic melanoma cells in a three-dimensional human skin equivalent model. PeerJ. 5: e3754. - W. Jin, C.J. Penington, S.W. McCue and
**M.J. Simpson**(2017). A computational modelling framework to quantify the effects of passaging cell lines . PLOS ONE. 12: e0181941. - A.P. Browning, S.W. McCue and
**M.J. Simpson**(2017). A Bayesian computational approach to explore the optimal duration of a cell proliferation assay . Bulletin of Mathematical Biology. 79: 1888-1906. - P. Haridas, C.J. Penington, J.A. McGovern, D.L.S. McElwain and
**M.J. Simpson**(2017). Quantifying rates of cell migration and cell proliferation in co-culture barrier assays reveals how skin and melanoma cells interact during melanoma spreading and invasion. Journal of Theoretical Biology. 423: 13-25. - O.M. Matsiaka, C.J. Penington, R.E. Baker and
**M.J. Simpson**(2017). Continuum approximations for lattice-free multi-species models of collective cell migration. Journal of Theoretical Biology. 422: 1-11. - W. Jin, E.T. Shah, C.J. Penington, S.W. McCue, P.K. Maini and
**M.J. Simpson**(2017). Logistic proliferation of cells in scratch assays is delayed. Bulletin of Mathematical Biology. 79: 1028-1050. - M. Zheng, F. Liu, Q. Liu, K. Burrage and
**M.J. Simpson**(2017). A novel numerical approximation of the time fractional reaction-diffusion equation with a moving boundary. Journal of Computational Physics. 338: 493-510. **M.J. Simpson**, K-Y. Lo and Y-S. Sun (2017). Quantifying the roles of random motility and directed motility using advection-diffusion theory for a 3T3 fibroblast cell migration assay stimulated with an electric field. BMC Systems Biology. 11:39.- S.T. Johnston, R.E. Baker and
**M.J. Simpson**(2017). A new and accurate continuum description of moving fronts. New Journal of Physics. 19: 033010. - S.T. Johnston, R.E. Baker, D.L.S. McElwain and
**M.J. Simpson**(2017). Co-operation, competition and crowding: a discrete framework linking Allee kinetics, nonlinear diffusion, shocks and sharp-fronted travelling waves. Scientific Reports. 7: 42134. **M.J. Simpson**(2017). Critical time scales for morphogen gradient formation: Concentration or gradient criteria. International Journal of Heat and Mass Transfer. 106: 570-572.- F. Jazaei,
**M.J. Simpson**and T.P. Clement (2017). Understanding time scales of diffusive fluxes and the implication for steady state and steady shape conditions. Geophysical Research Letters. 44: 174-180. - W. Jin, C.J. Penington, S.W. McCue and
**M.J. Simpson**(2016). Stochastic simulation tools and continuum models for describing two-dimensional collective cell spreading with universal growth functions. Physical Biology. 13: 056003. - A.J. Ellery, R.E. Baker and
**M.J. Simpson**(2016). An analytical method for disentangling the roles of adhesion and crowding for random walk models on a crowded lattice. Fast Track Letter, Physical Biology. 13: 05LT02. - P.R. Taylor, R.E. Baker,
**M.J. Simpson**and C.A. Yates (2016). Coupling volume-excluding compartment-based models of diffusion at different scales: Voronoi and pseudo-comparment approaches. Journal of the Royal Society Interface. 13: 2016336. - C.J. Penington, R.E. Baker and
**M.J. Simpson**(2016). Exits in order: how crowding affects particle lifetimes. The Journal of Chemical Physics. 144: 244107. - C.J. Andrews, L. Cuttle and
**M.J. Simpson**(2016). Quantifying the role of burn temperature, burn duration and skin thickness in an*in vivo*animal skin model of heat conduction. International Journal of Heat and Mass Transfer. 101: 542-549. - A.J. Ellery, R.E. Baker and
**M.J. Simpson**(2016). Distinguishing between short-time non-Fickian diffusion, and long-time Fickian diffusion for a random walk on a crowded lattice. Communication, The Journal of Chemical Physics. 144: 171104. - S.T. Johnston, R.E. Baker and
**M.J. Simpson**(2016). Filling the gaps: A robust description of adhesive birth-death-movement processes. Physical Review E. 93: 042413. - S.T. Johnston, J.V. Ross, B.J. Binder, D.L.S. McElwain, P. Haridas and
**M.J. Simpson**(2016). Quantifying the effect of experimental design choices for*in vitro*scratch assays. Journal of Theoretical Biology. 400: 19-31. - P. Haridas, J.A. McGovern, A.S. Kashyap, D.L.S. McElwain and
**M.J. Simpson**(2016). Standard melanoma-associated markers do not identify the MM127 metastatic melanoma cell line. Scientific Reports. 6: 24569. - R.N. Binny, P. Haridas, A. James, R. Law,
**M.J. Simpson**and M.J. Plank (2016). Spatial structure arising from neighbour-dependent bias in collective cell movement. PeerJ. 4: e1689. - B.J. Binder and
**M.J. Simpson**(2016). Cell density and cell size dynamics during*in vitro*tissue growth experiments: Implications for mathematical models of collective cell behaviour. Applied Mathematical Modelling. 40: 3438-3446. - A.J. Ellery, R.E. Baker, S.W. McCue and
**M.J. Simpson**(2016). Modeling transport through an environment crowded by a mixture of obstacles of different shapes and sizes. Physica A: Statistical Mechanics and its Applications. 449: 74-84. - W. Jin, E.T. Shah, C.J. Penington, S.W. McCue, L.K. Chopin and
**M.J. Simpson**(2016). Reproducibility of scratch assays is affected by the initial degree of confluence: expeirments, modelling and model selection. Journal of Theoretical Biology. 390: 136-145. - F. Jazaei,
**M.J. Simpson**and T.P. Clement (2016). Spatial analysis of aquifer response times for radial flow processes: Nondimensional analysis and laboratory-scale tests. Journal of Hydrology. 532: 1-8. - C. Irons, M.J. Plank and
**M.J. Simpson**(2016). Lattice-free models of directed cell motility. Physica A: Statistical Mechanics and its Applications. 442: 110-121. - A.J. Ellery, R.E. Baker and
**M.J. Simpson**(2015). Calculating the Fickian diffusivity for a lattice-based random walk with agents and obstacles of different shapes and sizes. Physical Biology. 12: 066010. - P.R. Taylor, C.A. Yates,
**M.J. Simpson**and R.E. Baker (2015). Reconciling transport models across scales: the role of volume exclusion. Rapid Communication, Physical Review E. 92: 040701(R). **M.J. Simpson**, J.A. Sharp, L.C. Morrow and R.E. Baker (2015). Exact solutions of coupled multispecies linear reaction-diffusion equations on a uniformly growing domain. PLOS ONE. 10(9): e0138894.**M.J. Simpson**and R.E. Baker (2015). Exact calculations of survival probability for diffusion on growing lines, disks and spheres: the role of dimension. The Journal of Chemical Physics. 143, 094109.- S.T. Johnston, E.T. Shah, L.K. Chopin, D.L.S. McElwain and
**M.J. Simpson**(2015). Estimating cell diffusivity and cell proliferation rate by interpreting IncuCyte ZOOM assay data using the Fisher-Kolmogorov model. BMC Systems Biology. 9, 38. **M.J. Simpson**and L.C. Morrow (2015). Analytical model of reactive transport processes with spatially variable coefficients. Royal Society Open Science. 2, 140348.**M.J. Simpson**and R.E. Baker (2015). Spatial moment techniques for modelling biological processes. Bulletin of Mathematical Biology. 77, 581 - 585.- D.C. Markham,
**M.J. Simpson**and R.E. Baker (2015). Choosing an appropriate modelling framework for analysing multispecies co-culture experiments. Bulletin of Mathematical Biology. 77, 713-734. **M.J. Simpson**, J.A. Sharp and R.E. Baker (2015). Survival probability for a diffusive process on a growing domain. Physical Review E. 91, 042701.- B.N. Vo, C.C. Drovandi, A.N Pettitt and
**M.J. Simpson**(2015). Quantifying uncertainty in parameter estimates for stochastic models of collective cell spreading using approximate Bayesian computation. Mathematical Biosciences. 263, 133 - 142. **M.J. Simpson**(2015). Exact solutions of linear reaction-diffusion processes on a uniformly growing domain: Criteria for successful colonization. PLOS ONE. 10(2): e0117949.- S.T. Johnston,
**M.J. Simpson**and R.E. Baker (2015). Modelling the movement of interacting cell populations: A moment dynamics approach. Journal of Theoretical Biology, 370, 81 - 92. - B.J Binder and
**M.J. Simpson**(2015). Spectral analysis of pair-correlation bandwidth: Application to cell biology images. Royal Society Open Science, 2, 140494. **M.J. Simpson**and S.W. McCue (2015). ANZIAM 2015. Gazette of the Australian Mathematical Society. 42, 23 - 25.- F. Jazaei,
**M.J. Simpson**and T.P. Clement (2014). An analytical framework for quantifying aquifer response time scales associated with transient boundary conditions. Journal of Hydrology, 519, 1642 - 1648. - S.T Johnston,
**M.J. Simpson**, D.L.S. McElwain, B.J. Binder and J.V. Ross (2014). Interpreting scratch assays using pair density dynamics and approximate Bayesian computation. Royal Society Open Biology, 4, 140097. - K.K. Treloar,
**M.J. Simpson**, B.J. Binder, D.L.S McElwain and R.E. Baker (2014). Assessing the role of spatial correlations during collective cell spreading. Scientific Reports, 4, 5713. - S.T. Johnston,
**M.J. Simpson**and D.L.S McElwain (2014). How much information can be obtained from tracking the position of the leading edge in a scratch assay? Journal of the Royal Society Interface, 11, 20140325. - K.K. Treloar,
**M.J. Simpson**, D.L.S McElwain and R.E Baker (2014). Are*in vitro*estimates of cell diffusivity and cell proliferation rate sensitive to assay geomentry? Journal of Theoretical Biology, 356, 71 - 84. - H.M. Young, A.J. Bergner,
**M.J. Simpson**, S.J. McKeown, M.M. Hao, C.R. Anderson and H. Enomoto (2014). Colonizing while migrating: How do individual enteric neural crest cells behave? BMC Biology, 12. 23. **M.J. Simpson**and A.J. Ellery (2014). Exact series solutions of reactive transport models with general initial conditions. Journal of Hydrology. 513, 7 - 12.- D.J.G. Agnew, J.E.F. Green, T.M. Brown,
**M.J. Simpson**and B.J. Binder (2014). Distinguishing between mechanisms of cell aggregation using pair-correlation functions. Journal of Theoretical Biology. 352, 16 - 23. - D.C. Markham,
**M.J. Simpson**, P.K. Maini, E.A. Gaffney and R.E. Baker (2014). Comparing methods for modelling spreading cell fronts. Journal of Theoretical Biology. 353, 95 - 103. - A.J. Ellery,
**M.J. Simpson**, S.W. McCue and R.E. Baker (2014). Characterizing transport through a crowded environment with different obstacle sizes. The Journal of Chemical Physics. 140, 054108. **M.J. Simpson**, P. Haridas and D.L.S. McElwain (2014). Do pioneer cells exist? PLOS ONE.9(1): e85488.**M.J. Simpson**, J.A Sharp and R.E. Baker (2014). Distinguishing between mean-field, moment dynamics and stochastic descriptions of birth-death-movement processes. Physica A: Statistical Mechanics and its Applications. 395, 236 - 246.- K.K. Treloar,
**M.J. Simpson**, P. Haridas, K.J. Manton, D.I. Leavesley, D.L.S. McElwain and R.E. Baker (2013). Multiple types of data are required to identify the mechanisms influencing the spatial expansion of melanoma cell colonies. BMC Systems Biology. 7, 137. - S.T. Johnston,
**M.J. Simpson**and M.J. Plank (2013). Lattice-free descriptions of collective motion with crowding and adhesion. Physical Review E. 88, 062720. - A.J. Ellery,
**M.J. Simpson**, S.W. McCue and R.E. Baker (2013). A simplified approach for calculating the moments of action for linear reaction-diffusion equations. Physical Review E. 88, 054102. - D.C. Markham,
**M.J. Simpson**, P.K. Maini, E.A. Gaffney and R.E. Baker (2013). Incorporating spatial correlations into multi-species mean-field models. Physical Review E. 88, 052713. **M.J. Simpson**, F. Jazaei and T.P. Clement (2013). How long does it take for aquifer recharge or aquifer discharge processes to reach steady state? Journal of Hydrology. 501, 241 - 248.- L.G. Bowden,
**M.J. Simpson**and R.E. Baker (2013). Design and interpretation of cell trajectory assays. Journal of the Royal Society Interface. 10, 20130630. - M.J. Plank and
**M.J. Simpson**(2013). Lattice-free models of cell invasion: discrete simulations and travelling waves. Bulletin of Mathematical Biology. 75, 2150 - 2166. - B.J. Binder and
**M.J. Simpson**(2013). Quantifying spatial stucture in experimental observations and agent-based simulations using pair-correlation functions. Physical Review E. 88, 022705. - A.J. Ellery,
**M.J. Simpson**and S.W. McCue (2013). Comment on Local accumulation times for source, diffusion and degradation models in two and three dimensions. The Journal of Chemical Physics. 139, 017101. - D.C. Markham,
**M.J. Simpson**and R.E. Baker (2013). Simplified method for including spatial correlations in mean-field approximations. Physical Review E. 87, 062702. - K.K.Treloar and
**M.J.Simpson**(2013). Sensitivity of edge detection methods for quantifying cell migration assays. PLOS ONE. 8(6): e67389. **M.J.Simpson**, B.H.Foy and S.W.McCue (2013). Travelling waves for a velocity-jump model of cell migration and proliferation. Mathematical Biosciences. 244, 98 - 106.**M.J.Simpson**, B.J.Binder, P.Haridas, B.K.Wood, K.K.Treloar, D.L.S.McElwain and R.E.Baker (2013). Experimental and modelling investigations of monolayer development with clustering. Bulletin of Mathematical Biology. 75, 871 - 889.**M.J.Simpson**, K.K.Treloar, B.J.Binder, P.Haridas, K.J.Manton, D.I.Leavesley, D.L.S.McElwain and R.E.Baker (2013). Quantifying the roles of cell motility and cell proliferation in a circular barrier assay. Journal of the Royal Society Interface. 10, 20130007.- K.K.Treloar,
**M.J.Simpson**and S.W.McCue (2013). Velocity-jump processes with proliferation. Journal of Physics A: Mathematical and Theoretical. 46, 015003. Highlighted by IOP Insights. **M.J.Simpson**, A.J.Ellery, S.W.McCue and R.E.Baker (2013). Critical timescales and time intervals for coupled linear processes. ANZIAM Journal. 54, 127 - 142.- A.J.Ellery,
**M.J.Simpson**, S.W.McCue and R.E.Baker (2012). Moments of action provide insight into critical times for advection-diffusion-reaction processes. Physical Review E. 86, 031136. **M.J.Simpson**and G.N.Mercer (2012). Infectious disease modelling. ANZIAM Journal. 54, 1 - 2.- B.J.Binder, J.V.Ross and
**M.J.Simpson**(2012). A hybrid model for studying spatial aspects of infectious diseases. ANZIAM Journal. 54, 37 - 49. - S.T.Johnston,
**M.J.Simpson**and R.E.Baker (2012). Mean-field descriptions of collective migration with strong adhesion. Physical Review E. 85, 051922. - M.J.Plank and
**M.J.Simpson**(2012). Models of collective cell behaviour with crowding effects: comparing lattice-based and lattice-free approaches. Journal of the Royal Society Interface. 9, 2983 - 2996. - A.J.Ellery,
**M.J.Simpson**, S.W.McCue and R.E.Baker (2012). Critical timescales for advectionâ€“diffusionâ€“reaction processes. Physical Review E. 85, 041135. - R.E.Baker and
**M.J.Simpson**(2012). Models of collective cell motion for cell populations with different aspect ratio: diffusion, proliferation and travelling waves. Physica A: Statistical Mechanics and its Applications. 391, 3729 - 3750. **M.J.Simpson**and A.J.Ellery (2012). An analytical solution for diffusion and nonlinear uptake of oxygen in a spherical cell. Applied Mathematical Modelling. 36: 3329 - 3334.- K.K.Treloar,
**M.J.Simpson**and S.W.McCue (2011). Velocity-jump models with crowding effects. Physical Review E. 84, 061920. - S.W.Chang, T.P.Clement,
**M.J.Simpson**and K-K.Lee (2011). Does sea-level rise have an impact on saltwater intrusion? Advances in Water Resources. 34: 1283 - 1291. **M.J.Simpson**and R.E.Baker (2011). Corrected mean-field models for spatially-dependent advection-diffusion-reaction phenomena. Physical Review E. 83, 051922.- A.J.Ellery and
**M.J.Simpson**(2011). An analytical method to solve a general class of nonlinear reactive transport models. Chemical Engineering Journal. 169: 313-318. **M.J.Simpson**, R.E.Baker and S.W.McCue (2011). Models of collective cell spreading with variable cell aspect ratio: A motivation for degenerate diffusion models. Physical Review E. 83, 021901.**M.J.Simpson**, C.Towne, D.L.S.McElwain and Z.Upton (2010). Migration of breast cancer cells: Understanding the roles of volume exclusion and cell-to-cell adhesion. Physical Review E. 82, 041901.- R.E.Baker and
**M.J.Simpson**(2010). Correcting mean-field approximations for birth-death-movement processes. Physical Review E. 82, 041905. **M.J.Simpson**, K.A.Landman and B.D.Hughes (2010). Cell invasion with proliferation mechanisms motivated by time-lapse data. Physica A: Statistical Mechanics and its Applications. 389: 3779 - 3790.- A.E.Fernando, K.A.Landman and
**M.J.Simpson**(2010). Nonlinear diffusion and exclusion processes. Physical Review E. 81, 011903. **M.J.Simpson**, K.A.Landman, B.D.Hughes and A.E.Fernando (2010). A model for mesoscale patterns in motile populations. Physica A: Statistical Mechanics and its Applications. 389: 1412 - 1424.**M.J.Simpson**, B.D.Hughes and K.A.Landman (2009). Diffusing populations: Ghosts or Folks? Australasian Journal of Engineering Education. 15: 59-68.**M.J.Simpson**, K.A.Landman and B.D.Hughes (2009). Pathlines in exclusion processes. Physical Review E. 79, 031920.**M.J.Simpson**(2009). Depth-averaging errors in reactive transport modelling. Water Resources Research. 45, W02505.**M.J.Simpson**, K.A.Landman and B.D.Hughes (2009). Distinguishing between directed and undirected cell motility within an invading cell population. Bulletin of Mathematical Biology, 71: 781-799.**M.J.Simpson**, K.A.Landman and B.D.Hughes (2009). Multi-species simple exclusion processes. Physica A: Statistical Mechanics and its Applications, 388: 399-406.- B.J.Binder, K.A.Landman,
**M.J.Simpson**, M.Mariani and D.F.Newgreen (2008). Modeling proliferative tissue growth: a general approach and an avian case study. Physical Review E. 78, 031912. - K.A.Landman,
**M.J.Simpson**and G.J.Pettet (2008). Tactically-driven nonmonotone travelling waves. Physica D: Nonlinear Phenomena. 237: 678-691. **M.J.Simpson**and K.A.Landman (2008). Theoretical analysis and physical interpretation of temporal truncation errors in operator split algorithms. Mathematics and Computers in Simulation, 77: 9-21.**M.J.Simpson**(2008). Discussion of Direct and split operator approaches with ELLAM for reactive transport equations. AIChE Journal, 54(2): 588-588.**M.J.Simpson**, A.Merrifield, K.A.Landman and B.D.Hughes (2007). Simulating invasion with cellular automata: connecting cell-scale and population-scale properties. Physical Review E. 76, 021918.**M.J.Simpson**and K.A.Landman (2007). Nonmonotone chemotactic invasion: High-resolution simulations, phase plane analysis and new benchmark problems. Journal of Computational Physics, 225(1): 6-12.**M.J.Simpson**and K.A.Landman (2007). Analysis of split operator methods applied to reactive transport with Monod kinetics. Advances in Water Resources, 30(9): 2026 - 2033.**M.J.Simpson**, K.A.Landman and K.Bhaganagarapu (2007). Coalescence of interacting cell populations. Journal of Theoretical Biology, 247: 525-543.- K.A.Landman,
**M.J.Simpson**and D.F.Newgreen (2007). Mathematical and experimental insight into the development of the enteric nervous system and Hirschsprung's Disease. Development, Growth and Differentiation, 49: 277-286. **M.J.Simpson**, D.C.Zhang, M.Mariani, K.A.Landman and D.F.Newgreen (2007). Cell proliferation drives neural crest cell invasion of the intestine. Developmental Biology, 302: 553-568. (Cover illustration article).**M.J.Simpson**(2007). Reply to comment on Computing residence times for flow towards a pumping well: Nomograph solution and validity of the small draw-down approximation. Hydrogeology Journal, 15: 431-432.**M.J.Simpson**, K.A.Landman, B.D.Hughes and D.F.Newgreen (2006). Looking inside an invasion wave of cells using continuum models: Proliferation is the key. Journal of Theoretical Biology, 243: 343-360.**M.J.Simpson**, K.A.Landman and D.F. Newgreen (2006). Chemotactic and diffusive migration on a non-uniformly growing domain: Numerical algorithm development and applications. Journal of Computational and Applied Mathematics, 192(2): 282-300.**M.J.Simpson**and K.A.Landman (2006). Characterizing and minimizing the operator split error for Fisher's equation. Applied Mathematics Letters, 19(7): 612-620.**M.J.Simpson**, T.P.Clement and F.E.Yeomans (2006). Erratum, Analytical model for computing residence times near a pumping well. Groundwater, 44(4): 509 - 510.**M.J.Simpson**, K.A.Landman and T.P.Clement (2005). Assessment of a non-traditional operator split algorithm for simulation of reactive transport. Mathematics and Computers in Simulation, 70(1): 44-60.**M.J.Simpson**(2005). Computing residence times for flow towards a pumping well: Nomograph solution and validity of the small draw-down approximation. Hydrogeology Journal, 13(5-6): 889 - 894.- K.A.Landman,
**M.J.Simpson**, J.L.Slater and D.F.Newgreen (2005). Diffusive and chemotactic cellular migration: smooth and discontinuous travelling wave solutions. SIAM Journal on Applied Mathematics, 65(4): 1420 - 1442. **M.J.Simpson**(2004). SEAWAT-2000: A Three-dimensional model for variable-density flow and transport processes. Groundwater, 42(5): 642 - 645.**M.J.Simpson**and T.P.Clement (2004). Improving the worthiness of the Henry problem as a benchmark for density-dependent ground water flow problems. Water Resources Research, 40(1) W01504.**M.J.Simpson**, T.P.Clement and F.E.Yeomans (2003). Analytical model for computing residence times near a pumping well. Groundwater, 41(3): 351 - 354.**M.J.Simpson**, T.P.Clement and T.A.Gallop (2003). Laboratory and numerical investigation of flow and transport near a seepage-face boundary. Groundwater, 41(5): 690 - 700.**M.J.Simpson**and T.P.Clement (2003). A theoretical analysis of the worthiness of Henry and Elder problems as benchmarks of density-dependent groundwater flow models. Advances in Water Resources, 26(1): 17-31.**M.J.Simpson**and T.P.Clement (2003). Comparison of finite difference and finite element solutions to the variably saturated flow equation. Journal of Hydrology, 270(1): 49 - 64.