List of publications

Paul Zegeling
  1. R.M. Furzeland, J.G. Verwer & P.A. Zegeling, "A Numerical Study of Three Moving Grid Methods for One-Dimensional Partial Differential Equations Which Are Based on the Method of Lines"; published in "Journal of Computational Physics" (V89, pp. 349-388, 1990) [pdf].

  2. F. Verhulst & P.A. Zegeling, "An Asymptotic-Numerical Approach to the Coronal Loop Problem"; published in "Mathematical Methods in the Applied Sciences" (V13, pp. 431-439, 1990) [pdf].

  3. J.G. Verwer, J.G. Blom, R.M. Furzeland & P.A. Zegeling, "A Moving-Grid Method for One-Dimensional PDEs Based on the Method of Lines"; published in "Adaptive Methods for Partial Differential Equations", eds. J.E. Flaherty, P.J. Paslow, M.S. Shepherd & J.D. Vasilakis, SIAM 1989 [weblink] .

  4. J.G. Blom & P.A. Zegeling, "Algorithm 731: A Moving-Grid Interface for Systems of One-Dimensional Time-Dependent Partial Differential Equations"; published in "ACM Transactions in Mathematical Software" (1994, V20, N2, pp. 194-214). [pdf] [SOFTWARE AVAILABLE!].

  5. P.A. Zegeling & J.G. Blom, "An Evaluation of the Gradient-Weighted Moving-Finite-Element Method in One Space Dimension"; published in "Journal of Computational Physics" (V103, N2, pp. 422-441, 1992). [pdf].

  6. P.A. Zegeling & J.G. Blom, "A Note on the Grid Movement Induced by MFE"; published in "International Journal for Numerical Methods in Engineering" (V35, N3, pp. 623-636, 1992) [pdf].

  7. J.C.H. v. Eijkeren, P.A. Zegeling & S.M. Hassanizadeh, "Practical Use of SPRINT and a Moving Grid Interface for a Class of 1D Non-Linear Transport Problems", RIVM-report 959101001, Rijksinstituut voor Volksgezondheid en Milieuhygiene, Bilthoven, 1991.

  8. P.A. Zegeling, J.G. Verwer & J.C.H v. Eijkeren, "Application of a Moving-Grid Method to a Class of 1D Brine Transport Problems in Porous Media"; published in "International Journal for Numerical Methods in Fluids" (V15, N2, pp. 175-191, 1992) [pdf].

  9. P.A. Zegeling, "Moving-Finite-Element Solution of a 2D Brine Transport Problem in a Porous Medium"; published in "Advances in Computer Methods for Partial Differential Equations - VII, eds. R. Vichnevetsky, D. Knight and G. Richter, IMACS publication, pp. 845 - 851, 1992.

  10. P.A. Zegeling, "Moving-Finite-Element Solution of Time-Dependent Partial Differential Equations in Two Space Dimensions"; published in "Computational Fluid Dynamics" (V1, pp. 135-159, 1993) [weblink] .

  11. P.A. Zegeling, "Moving-Grid Methods for Time-Dependent Partial Differential Equations", published as [CWI-tract No. 94, Centre for Mathematics and Computer Science, Amsterdam, 1993] .

  12. P.A. Zegeling, "MFE revisited, Part I: Adaptive Grid-Generation using the Heat Equation", Preprint nr.946, Department of Mathematics, Utrecht University, 1996.

  13. P.A. Zegeling, "A Dynamically-Moving Adaptive Grid Method Based on a Smoothed Equidistribution Principle along Coordinate Lines", Proceedings of the 5th International Conference on Numerical Grid Generation in Computational Field Simulations, eds. B.K. Soni, J.F. Thompson, J. Häuser and P. Eiseman, April 1996, Mississippi State University.

  14. P.A. Zegeling, "Numerical Solution of Advection-Dispersion Models Using Dynamically-Moving Adaptive Grids"; published in the Proceedings of XIth Inter national Conference on Computational Methods in Water Resources, Canc\'{u}n, Mexico, July 1996.

  15. A. Doelman, T.J. Kaper & P.A. Zegeling, "Pattern formation in the 1-D Gray-Scott model"; published in Nonlinearity, 10 (1997) 523-563. [pdf].

  16. P.A. Zegeling, M. Borsboom & J.A.Th.M. van Kester, "Adaptive Moving-Grid Solutions of Shallow-Water Transport Models with Steep Vertical Gradients"; published in the Proceedings of the XIIth International Conference on Computational Methods in Water Resources, The Chersonese, Crete, Greece, June 15-19, 1998 [weblink] .

  17. P.A. Zegeling, "An Adaptive Moving Grid Method for PDE Models with Third and Fourth Order Spatial Derivatives"; published in the Proceedings of the 6th International Conference on Numerical Grid Generation in Computational Field Simulations, Univ. of Greenwich, United Kingdom, July 6-9, 1998.

  18. P.A. Zegeling, "R-refinement with Finite Elements or Finite Differences for Evolutionary PDE Models" [pdf]; published in the journal "Applied Numerical Mathematics", V26, N1-2, pp. 97-104, 1998.

  19. P.A. Zegeling, "Moving grid techniques", Chapter 37 in Handbook of Grid Generation, Eds. Joe F. Thompson, Bharat K. Soni, Nigel P. Weatherill, CRC Press LLC 1999.

  20. A.R. Champneys, P.J. McKenna & P.A. Zegeling, "Solitary Waves in Nonlinear Beam Equations; Stability, Fission and Fusion" [pdf]; published in "Nonlinear Dynamics", V21, pp. 31-53, 2000.

  21. R. Keppens, M. Nool, P.A. Zegeling & J.P. Goedbloed, "Dynamic Grid Adaptation for Computational Magnetohydrodynamics"; published in the Proceedings of HPCN Europe 2000: 61-70 [pdf] .

  22. P.A. Zegeling & R. Keppens, "Adaptive Method of Lines for Magnetohydrodynamic PDE Models" [pdf], a chapter in the book "Adaptive Method of Lines", CRC Press, 2001.

  23. P.A Zegeling & H.P. Kok, "Adaptive Moving Mesh Computations for Reaction-Diffusion Systems" [pdf], in the Proceedings of ACOMEN 2002, Second International Conference on Advanced Computational Methods in Engineering, held at Liege University, Belgium, May 28-31, 2002; published in J. of Comp. & Appl. Maths. (2004), 168, 519-528.

  24. P. Saucez, A. Vande Wouwer, W.E. Schiesser & P.A. Zegeling, "Method of Lines Study of Nonlinear Dispersive Waves" [pdf], in the Proceedings of ACOMEN 2002, Second International Conference on Advanced Computational Methods in Engineering, held at Liege University, Belgium, May 28-31, 2002; published in J. of Comp. & Appl. Maths (2004), 168, 413-423.

  25. P.A. Zegeling "Tensor-Product Adaptive Grids Based on Coordinate Transformations" [pdf], pp. 285-290 in the Proceedings of BAIL 2002, An International Conference on Boundary and Internal Layers; Computational and Asymptotic Methods, Eds. S. Wang & N. Fowkes, held at the University of Western Australia, Perth, WA, 8-12 July, 2002; published in J. of Comp. & Appl. Maths. 166 (2004), 343-360.

  26. P. Saucez, A. Vande Wouwer & P.A. Zegeling "Adaptive Method of Lines Solutions for the Extended Fifth Order Korteweg-De Vries Equation" [pdf]; published in J. of Comp. & Appl. Maths. 183 (2005), 343-357.

  27. P.A. Zegeling "On Resistive MHD Models with Adaptive Moving Meshes" [pdf]; published in J. of Scientific Computing 24 (2005), 263-284.

  28. P.A. Zegeling, W. de Boer & H. Tang "Robust and Efficient Adaptive Moving Mesh Solution of the 2-D Euler Equations" [pdf]; published in Contemporary Mathematics 383 (2005), 419-430.

  29. H. Berestycki, O. Diekmann, C.J. Nagelkerke & P.A. Zegeling "Can a Species Keep Pace with a Shifting Climate?" [pdf]; published in Bulletin of Mathematical Biology, 2009 Feb; 71(2):399-429.

  30. R.M.J. Schielen, T. van Leeuwen & P.A. Zegeling "Numerical Simulation of Alternating Bars in Straight Channels"; published in Proceedings of RCEM2005 (The 5th IAHR Symposium on River, Coastal and Estuarine Morphodynamics) held October 4-7 in Urbana, Illinois (2005) [weblink] .

  31. A. van Dam & P.A. Zegeling "A Robust Moving Mesh Finite Volume Method Applied to 1D Hyperbolic Conservation Laws from Magnetohydrodynamics" [pdf]; published in J. of Comput. Phys. 216 (2006), 526-546.

  32. P.A. Zegeling "Theory and Application of Adaptive Moving Grid Methods" ; published in the book "Adaptive Computations: Theory and Algorithms", edited by T. Tang and J. Xu (March 2007) [weblink].

  33. A. van Dam & P.A. Zegeling. "Mesh speeds versus solution interpolation - making moving mesh results sharper"; published in proceedings of ICFD'07, Reading, UK, March 2007.

  34. R.C. Wieggers, W.J. Goedheer, M.R. Akdim, F. Bijkerk & P.A. Zegeling "A Particle-In-Cell plus Monte-Carlo study of plasma-induced damage of normal incidence collector optics in extreme ultraviolet lithography" [pdf]; published in J. Appl. Phys. 103, 013308 (2008).

  35. V. Creigen, L. Ferracina, A. Hlod, S. van Mourik, K. Sjauw, V. Rottschaefer, M. Vellekoop & P.A. Zegeling "Modelling of a heart pump"; published in the Proceedings of SWI 2007 [pdf].

  36. P.A. Zegeling, I. Lagzi & F. Izsak "Transition of Liesegang precipitation systems: simulations with an adaptive grid PDE method"; published in Communications in Computational Physics, Vol. 10, No. 4 (2011), 867-881 [pdf].

  37. A. van Dam & P.A. Zegeling "Balanced monitoring of flow phenomena in moving mesh methods"; published in Commun. Comput. Phys. 7 (2010), 138-170 [pdf].

  38. A. ten Cate, B.J. Geurts, M. Muskulus, D. Koester, A. Muntean, J. van Opheusden, A. Peschansky, B. Vreman, P.A. Zegeling "Modeling and simulation of phase-transitions in multicomponent aluminum alloy casting"; published in Proceedings of SWI 2008 [pdf].

  39. F. Doster, P.A. Zegeling & R. Hilfer "Numerical Solutions of a Generalized Theory for Macroscopic Capillarity"; published in Physical Review E81, 1 (2010) [pdf].

  40. G. Hu & P.A. Zegeling "Simulating Finger Phenomena in Porous Media with a Moving Finite Element method"; published in Journal of Computational Physics, 2011 [pdf].

  41. R. Hilfer, F. Doster & P.A. Zegeling "Nonmonotone Saturation Profiles for Hydrostatic Equilibrium in Homogeneous Porous Media"; published in Vadose Zone Journal, V11, N3, 2012 [pdf].

  42. R.D. Haynes, W. Huang & P.A. Zegeling "A Numerical Study of Blowup in the Harmonic Map heat Flow Using the MMPDE Moving Mesh Method"; published in Numerical Mathematics:Theory,Methods and Applications, V6, N2, 2013 [pdf].

  43. C.J. van Duijn, S.M. Hassanizadeh, I.S. Pop & P.A. Zegeling "Non-equilibrium Models for Two Phase Flow in Porous Media: the Occurence of Saturation Overshoots"; published in the Proceedings of the Fifth Int. Conf. on Application of Porous Media, Babes-Bolyai Univ., Cluj-Napoca, August 25-28, 2013 [pdf].

  44. R. Kelling, J. Bickel, U. Nieken & P.A. Zegeling "An adaptive moving grid method for solving convection dominated transport equations in chemical engineering"; published in Computers and Chemical Engineering 71 (2014) 467–477 [pdf].

  45. P.A. Zegeling"An adaptive grid method for a non-equilibrium PDE model from porous media"; published in the Journal of Mathematical Study, V48, No.2, pp. 93-104, 2015 [pdf].

  46. R. Hilfer, O. Hoenig, F. Doster & P.A. Zegeling "Non-monotone travelling wave fronts in a system of fractional flow equations from porous media"; published in Transport in Porous Media, DOI 10.1007/s11242-015-0618-2, pp 1-32 (2016) [pdf].

  47. P.A. Zegeling & I. Ates "A homotopy perturbation method for fractional-order convection-diffusion-reaction boundary-value problems"; published in Applied Mathematical Modelling, V47 (2017) 425–441 [pdf].

  48. H. Zhou & P.A. Zegeling "Stability and convergence analysis of a class of continuous piecewise polynomial approximations for time-fractional differential equations"; published in the Journal of Scientific Computing, 2 May, 2018 [pdf].

  49. H. Zhang & P.A. Zegeling "A numerical study of two-phase flow models with dynamic capillary pressure and hysteresis"; published in Transport in Porous Media, 116:825–846, December 2016 [pdf].

  50. P.A. Zegeling & S. Iqbal "Nonstandard finite differences for a truncated Bratu-Picard model"; published in Applied Mathematics and Computation, V324, pp.266-284, 2018 [pdf].

  51. H. Zhang & P.A. Zegeling "A moving mesh finite difference method for non-monotone solutions of non-equilibrium equations in porous media"; published in Communications in Computational Physics, February 2017 [pdf].

  52. H. Zhang & P.A. Zegeling "Numerical investigations of two-phase flow with dynamic capillary pressure in porous media via a moving mesh method"; published in Journal of Computational Physics; May 2017 [pdf].

  53. H. Zhang & P.A. Zegeling "Simulation of thin film flows with a moving mesh mixed finite element method"; published in Applied Mathematics and Computation, Volume 338, 1 December 2018, Pages 274-289; [pdf].

  54. P.A. Zegeling "A boundary-value method based on the explicit midpoint-method for semi-stable partial differential equations"; in preparation.

  55. S. Iqbal & P.A. Zegeling "Sixth-order adaptive non-uniform grids for singularly perturbed boundary-value problems"; to appear in the Lecture Notes in Computational Science and Engineering, Springer, 2019.

  56. H. Zhang, Y. Guo, W. Li & P.A. Zegeling "Runge-Kutta symmetric interior penalty discontinuous Galerkin methods for a modified Buckley-Leverett equation"; under review.

  57. S. Iqbal & P.A. Zegeling "An efficient nonlinear multigrid scheme for the 2D Bratu problem"; under review, 2019.

  58. P.A. Zegeling "An adaptive boundary-value approach for semi-stable ordinary differential equations"; in preparation.

  59. A. Zegeling & P.A. Zegeling "S-shaped bifurcations in a quadratic Hamiltonian system"; submitted to the journal Nonlinearity, 2019.

  60. S. Iqbal & P.A. Zegeling "Higher-order non-uniform grids for singularly perturbed convection-diffusion-reaction models"; to appear in the Journal of Computational Mathematics, 2019.

  61. J. Karkowski & P.A. Zegeling "Numerical bifurcation analysis of the Bratu model in n-dimensional cylindrical domains"; in preparation.

  62. L. v.d. Wiel & P.A. Zegeling "Adaptive grid computations for the fractional Gray-Scott model"; in preparation.

  63. M. Botchev & P.A. Zegeling "A method-of-lines approach for space-fractional heat equations"; in preparation.

  64. S. Iqbal & P.A. Zegeling "A numerical study of the higher-dimensional Gelfand-Bratu model"; to appear in the journal Computers and Mathematics with Applications, 2019.