List of publications
Paul Zegeling

R.M. Furzeland, J.G. Verwer & P.A. Zegeling, "A Numerical Study of Three Moving Grid Methods for OneDimensional Partial Differential Equations Which
Are Based on the Method of Lines"; published in "Journal of Computational Physics" (V89, pp. 349388, 1990) [pdf].

F. Verhulst & P.A. Zegeling, "An AsymptoticNumerical Approach to the Coronal Loop Problem"; published in "Mathematical Methods in the Applied Sciences" (V13, pp. 431439, 1990) [pdf].

J.G. Verwer, J.G. Blom, R.M. Furzeland & P.A. Zegeling, "A MovingGrid Method for OneDimensional 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] .

J.G. Blom & P.A. Zegeling, "Algorithm 731: A MovingGrid Interface for Systems of OneDimensional TimeDependent Partial Differential Equations"; published in "ACM Transactions in Mathematical Software" (1994, V20, N2, pp. 194214). [pdf] [SOFTWARE AVAILABLE!].

P.A. Zegeling & J.G. Blom, "An Evaluation of the GradientWeighted MovingFiniteElement Method in One Space Dimension"; published in "Journal of Computational Physics" (V103, N2, pp. 422441, 1992). [pdf].

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. 623636, 1992) [pdf].

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 NonLinear Transport Problems", RIVMreport 959101001, Rijksinstituut voor Volksgezondheid en Milieuhygiene, Bilthoven, 1991.

P.A. Zegeling, J.G. Verwer & J.C.H v. Eijkeren, "Application of a MovingGrid Method to a Class of 1D Brine Transport Problems in Porous Media"; published in "International Journal for Numerical Methods in Fluids" (V15, N2, pp. 175191, 1992) [pdf].

P.A. Zegeling, "MovingFiniteElement 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.

P.A. Zegeling, "MovingFiniteElement Solution of TimeDependent Partial Differential Equations in Two Space Dimensions"; published in "Computational Fluid Dynamics" (V1, pp. 135159, 1993) [weblink] .

P.A. Zegeling, "MovingGrid Methods for TimeDependent Partial Differential Equations", published as [CWItract No. 94, Centre for Mathematics and Computer Science, Amsterdam, 1993] .

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

P.A. Zegeling, "A DynamicallyMoving 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.

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

A. Doelman, T.J. Kaper & P.A. Zegeling, "Pattern formation in the 1D GrayScott model"; published in Nonlinearity, 10 (1997) 523563. [pdf].

P.A. Zegeling, M. Borsboom & J.A.Th.M. van Kester, "Adaptive MovingGrid Solutions of ShallowWater 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 1519, 1998 [weblink] .

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 69, 1998.

P.A. Zegeling, "Rrefinement with Finite Elements or Finite Differences for Evolutionary PDE Models" [pdf]; published in the journal "Applied Numerical Mathematics", V26, N12, pp. 97104, 1998.

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.

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. 3153, 2000.

R. Keppens, M. Nool, P.A. Zegeling & J.P. Goedbloed, "Dynamic Grid Adaptation for Computational Magnetohydrodynamics"; published in the Proceedings of HPCN Europe 2000: 6170 [pdf] .

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.

P.A Zegeling & H.P. Kok, "Adaptive Moving Mesh Computations for ReactionDiffusion Systems" [pdf], in the Proceedings of ACOMEN 2002, Second International Conference on Advanced Computational Methods in Engineering, held at Liege University, Belgium, May 2831, 2002; published in J. of Comp. & Appl. Maths. (2004), 168, 519528.

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 2831, 2002; published in J. of Comp. & Appl. Maths (2004), 168, 413423.

P.A. Zegeling "TensorProduct Adaptive Grids Based on Coordinate Transformations" [pdf], pp. 285290 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, 812 July, 2002; published in J. of Comp. & Appl. Maths. 166 (2004), 343360.

P. Saucez, A. Vande Wouwer & P.A. Zegeling "Adaptive Method of Lines Solutions for the Extended Fifth Order KortewegDe Vries Equation" [pdf]; published in J. of Comp. & Appl. Maths. 183 (2005), 343357.

P.A. Zegeling "On Resistive MHD Models with Adaptive Moving Meshes" [pdf]; published in J. of Scientific Computing 24 (2005), 263284.

P.A. Zegeling, W. de Boer & H. Tang "Robust and Efficient Adaptive Moving Mesh Solution of the 2D Euler Equations" [pdf]; published in Contemporary Mathematics 383 (2005), 419430.

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):399429.

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 47 in Urbana, Illinois (2005) [weblink] .

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), 526546.

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].

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.

R.C. Wieggers, W.J. Goedheer, M.R. Akdim, F. Bijkerk & P.A. Zegeling "A ParticleInCell plus MonteCarlo study of plasmainduced damage of normal incidence collector optics in extreme ultraviolet lithography" [pdf]; published in J. Appl. Phys. 103, 013308 (2008).

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].

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), 867881 [pdf].

A. van Dam & P.A. Zegeling "Balanced monitoring of flow phenomena in moving mesh methods"; published in Commun. Comput. Phys. 7 (2010), 138170 [pdf].

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 phasetransitions in multicomponent aluminum alloy casting"; published in Proceedings of SWI 2008 [pdf].

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

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].

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].

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].

C.J. van Duijn, S.M. Hassanizadeh, I.S. Pop & P.A. Zegeling "Nonequilibrium 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, BabesBolyai Univ., ClujNapoca, August 2528, 2013 [pdf].

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].

P.A. Zegeling"An adaptive grid method for a nonequilibrium PDE model from porous media"; published in the Journal of Mathematical Study, V48, No.2, pp. 93104, 2015 [pdf].

R. Hilfer, O. Hoenig, F. Doster & P.A. Zegeling "Nonmonotone travelling wave fronts in a system of fractional flow equations from porous media"; published in Transport in Porous Media, DOI 10.1007/s1124201506182, pp 132 (2016) [pdf].

P.A. Zegeling & I. Ates "A homotopy perturbation method for fractionalorder convectiondiffusionreaction boundaryvalue problems"; published in Applied Mathematical Modelling, V47 (2017) 425–441 [pdf].

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

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

P.A. Zegeling & S. Iqbal "Nonstandard finite differences for a truncated BratuPicard model"; published in Applied Mathematics and Computation, V324, pp.266284, 2018 [pdf].

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

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

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 274289; [pdf].

S. Iqbal & P.A. Zegeling "Sixthorder adaptive nonuniform grids for singularly perturbed boundaryvalue problems"; published in the Lecture Notes in Computational Science and Engineering, Volume 131, Springer, December 2018; [pdf].

H. Zhang, Y. Guo, W. Li & P.A. Zegeling "RungeKutta symmetric interior penalty discontinuous Galerkin methods for a modified BuckleyLeverett equation"; preprint, 2017.

S. Iqbal & P.A. Zegeling "An efficient nonlinear multigrid scheme for the 2D Bratu problem"; published in the journal Applied Mathematics and Computation, Volume 372, 2020; [pdf].

S. Iqbal & P.A. Zegeling "Higherorder nonuniform grids for singularly perturbed convectiondiffusionreaction models"; published in the journal Computational Mathematics and Mathematical Physics, Volume 59, N12, pages 20572079, 2019; [pdf].

S. Iqbal & P.A. Zegeling "A numerical study of the higherdimensional GelfandBratu model"; published in the journal Computers and Mathematics with Applications, Volume 79, pages 16191633, 2020; [pdf].

A. Zegeling & P.A. Zegeling "Sshaped bifurcations in a quadratic Hamiltonian system"; published in the Electronic Journal of Qualitative Theory of Differential Equations, Volume 49, 1–38, 2021; [pdf].

P.A. Zegeling "Adaptive grids for nonmonotone waves and instabilities in a nonequilibrium PDE model"; published in the Lecture Notes in Computational Science and Engineering, DOI: 10.1007/9783030767983_11, pages 179198, Springer, 2021 ; [pdf].

P.A. Zegeling & M.W.F. van Spengler"A generalized midpointbased BVmethod for unstable partial differential equations"; published in the Journal of Computational and Applied Mathematics, 424 (2023); [pdf].

P.A. Zegeling "Detecting twodimensional fingering patterns in a nonequilibrium PDE model via adaptive moving meshes"; published in Computational Mathematics and Mathematical Physics, Vol. 62, No. 8, pp. 1331–1344, 2022; [pdf].

C.J. Berends, R.S.W. van de Wal & P.A. Zegeling "Improvements on the discretisation of boundary conditions to the momentum balance for glacial ice"; submitted, 2023.

P. Yuan & P.A. Zegeling "A nonuniform L2discretization for the onedimensional spacefractional GrayScott system"; submitted, 2024.

P.A. Zegeling "A threedimensional adaptive moving mesh for ..."; in preparation, 2023.

P.A. Zegeling & L. v.d. Wiel "Adaptive meshes for spacefractional onedimensional reactiondiffusion PDEs"; in preparation, 2023.

P.A. Zegeling & ..."Energypreserving BVMs with periodic ..."; in preparation, 2023.

P.A. Zegeling "An adaptive boundaryvalue approach for semistable ordinary ..."; in preparation, 2023.

M. Botchev & P.A. Zegeling "A methodoflines approach based on FDmatrices for ..."; in preparation, 2023.

M.W.F. van Spengler & P.A. Zegeling"Unconditional stablity of generalized midpointbased boundary value methods with a fixed time step"; in preparation, 2023.