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List of Publications - Prof. Dr. Christiane Helzel

Journal Publications:

  1. B. Duong and C. Helzel, A kinetic-uid model describing sedimentation in suspensions of rod-like particles and its approximation by hyperbolic moment equations, Multiscale Methods and Simulation, 24(1): 214{246, 2026 
    URL: https://epubs.siam.org/doi/10.1137/25M1741169 , pdf
  2. C. Helzel and A. Porfetye, A fully discrete Active Flux method for the Euler equations comparing diff erent truly multi-dimensional evolution operators 2026, 
    URL: arXiv:2606.21303
  3. E. Chudzik, Helzel, C., and Porfetye, A., A fully discrete truly multi-dimensional active flux method for the two-dimensional Euler equations, to appear in SIAM J. Sci. Comput., 2026
  4. A. Porfetye, Z. Tang, S. Chu, C. Helzel and M. Lukacova-Medvid'ova, New fully discrete active flux methods with truly multi-dimensional evolution operators and WENO reconstruction, 2025, 
    URL: arXiv: 2512.16359.
  5. Y. Kiechle, E. Chudzik and C. Helzel, A Positivity Preserving Active Flux Method for the Vlasov-Poisson System, J. Comput. Phys., 524, 2025, 113693. 
    URL: https://www.sciencedirect.com/science/article/pii/S0021999124009410?via%3Dihub
  6. S. Dahm, J. Giesselmann and C. Helzel, Numerical Discretisation of Hyperbolic Systems of Moment Equations Describing Sedimentation in Suspensions of Rod-Like Particles, J. Comput. Physics, 513 (2024) 113162. 
    URL: https://www.sciencedirect.com/science/article/pii/S002199912400411X
  7. E. Chudzik, C. Helzel and M. Lukacova-Medvid'ova, Active Flux Methods for Hyperbolic Systems using the Method of Bicharacteristics, J. Sci. Comput., 99(1), 13, 2024.
    URL: Active Flux Methods for Hyperbolic Systems Using the Method of Bicharacteristics
  8. D. Calhoun, E. Chudzik, and C. Helzel, The Cartesian Grid Active Flux Method with Adaptive Mesh Re nement, J. Sci. Comp., 94, 2023
    URL: The Cartesian Grid Active Flux Method with Adaptive Mesh Refinement
  9. S. Dahm and C. Helzel, Hyperbolic Systems of Moment Equations Describing Sedimentation in Suspensions of Rod-Like Particles, Multiscale Methods and Simulation, 40(3): 1002-1039, 2022. 
    URL: https://epubs.siam.org/doi/10.1137/21M1464592 , pdf
  10. E. Chudzik, C. Helzel and D. Kerkmann, The Cartesian Grid Active Flux Method: Linear stability and bound preserving limiting, Applied Mathematics and Computation, 393: 125501, 2021.
    URL: https://www.sciencedirect.com/science/article/pii/S0096300320304598
  11. C. Helzel, A third order accurate Wave Propagation Method for hyperbolic partial differential equations, Communications on Applied Mathematics and Computation, 2: 403-427, 2020.
    URL: https://link.springer.com/article/10.1007/s42967-019-00056-3
  12. C. Helzel and M. Schneiders,  Numerical approximation of the Smoluchowski equation using radial basis functions, Journal of Computational Mathematics, 38: 176-194, 2020.
    URL: https://doc.global-sci.org/uploads/admin/article_pdf/20200224/b9bed8fe162c0390de754f5ce141da34.pdf
  13. C. Helzel, D. Kerkmann and L. Scandurra, A new ADER Method Inspired by the Active Flux Method, J. Sci. Comput., 80: 1463-1497, 2019.
    URL: https://doi.org/10.1007/s10915-019-00988-1
  14. C. Helzel and A. E. Tzavaras, A kinetic model for the sedimentation of rod-like particles, Multiscale Modelling & Simulation, 15: 500-536, 2017.
    URL: http://epubs.siam.org/doi/abs/10.1137/15M1023907
  15. C. Helzel and A. E. Tzavaras, A comparison of macroscopic models describing the collective response of sedimenting rod-like particles in shear flow, Physica D 337: 18-29, 2016.
    URL: http://dx.doi.org/10.1016/j.physd.2016.07.004
  16. P. Buchmüller, J. Dreher and C. Helzel, Finite volume WENO methods for hyperbolic conservation laws on Cartesian grids with adaptive mesh refinement, Applied Mathematics and Computation, 272: 460--478, 2016.
    URL: http://www.sciencedirect.com/science/article/pii/S0096300315003926
  17. P. Buchmüller and C. Helzel, Improved accuracy of high-order WENO finite volume methods on Cartesian Grids, J. Sci. Comput., 61: 343--368, 2014.
    URL: http://dx.doi.org/10.1007/s10915-014-9825-1
  18. C. Helzel, J. A. Rossmanith and B. Taetz, A high order unstaggered constrained transport method for the ideal magnetohydrodynamic equations based on the method of lines, SIAM J. Sci. Comput., 35: A623-A653, 2013.
    URL: http://dx.doi.org/10.1137/120870323
  19. M. J. Berger and C. Helzel, A simplified $h$-box method for embedded boundary grids, SIAM J. Sci. Comput., 34: A861--A888, 2012.
    URL: http://dx.doi.org/10.1137/110829398
  20. C. Helzel, J. A. Rossmanith, B. Taetz, An unstaggered constrained transport method for the 3d ideal magnetohydrodynamic equations, J. Comput. Phys, 230: 3803--3829, 2011.
    URL: http://dx.doi.org/10.1016/j.jcp.2011.02.009
  21. M. J. Berger, D. Calhoun, C. Helzel, R. J. LeVeque, A logically rectangular grid on the sphere with adaptive refinement, Phil. Trans. R. Soc. A 367: 4483--4496, 2009.
    URL: http://dx.doi.org/10.1098/rsta.2009.0168
  22. D. Calhoun, C. Helzel, A finite volume method for solving parabolic equations on logically Cartesian curved surface meshes, SIAM J. Sci. Comput., 31: 4066--4099, 2009.
    URL: http://dx.doi.org/10.1007/978-3-540-75712-2_31
  23. D. Calhoun, C. Helzel and R. J. LeVeque, Logically rectangular grids and finite volume methods for PDEs in circular and spherical domains, SIAM Review, 50: 723--752, 2008.
    URL: http://dx.doi.org/10.1137/060664094
  24. C. Helzel and F. Otto, Multiscale simulations for suspensions of rod--like molecules, J. Comput. Phys., 216: 52--75, 2006.
    URL: dx.doi.org/10.1016/j.jcp.2005.11.028
  25. C. Helzel, M. J. Berger and R. J. LeVeque,  A high-resolution rotated grid method for conservation laws with embedded geometries, SIAM J. Sci. Comput., 28: 785--809, 2005.
    URL: http://dx.doi.org/10.1137/S106482750343028X
  26. M. J. Berger, C. Helzel and R. J. LeVeque, h-box methods for the approximation of conservation laws on irregular grids, SIAM J. Numer. Anal., 41: 893-918, 2003.
    URL: http://dx.doi.org/10.1137/S0036142902405394
  27. C. Helzel, R. J. LeVeque and G. Warnecke, A modified fractional step method for the accurate approximation of detonation waves, SIAM J. Sci. Comput., 22: 1489-1510, 2000.
    URL: http://dx.doi.org/10.1137/S1064827599357814
  28. C. Helzel and K. Petras,  Numerical estimation of projection constants, Numer. Funct. Anal. and Optimiz. 18 (5 & 6), 555-566, 1997.
    URL: www.tandfonline.com/doi/abs/10.1080/01630569708816778

Book Chapters:

  1. C. Helzel and R. J. LeVeque, Numerical Approximation of Stiff Reacting Flow, invited submission to a volume on Numerical Methods for Balance Laws (G. Puppo and G. Russo, eds.) quaderni di mathematica, vol. 24, 2010.
  2. C. Helzel and G. Warnecke, Unconditionally stable explicit schemes for the approximation of conservation laws, in Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, B.Fiedler (editor), Springer 2001.
    URL: https://link.springer.com/chapter/10.1007/978-3-642-56589-2_31

Proceedings:

  1. C. Helzel and D. Kerkmann, An Active Flux Method for Cut Cell Grids, In: Klöfkorn R., Keilegavlen E., Radu F., Fuhrmann J. (eds) Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects,  Examples. FVCA 2020. Springer Proceedings in Mathematics & Statistics, vol 323.
    URL: https://link.springer.com/chapter/10.1007/978-3-030-43651-3_47
  2. P. Buchmüller, J. Dreher and C. Helzel, Improved accuracy of high-order WENO finite volume methods on Cartesian grids with adaptive mesh refinement, in C.Klingenberg and M.Westdickenberg (eds.), Theory, Numerics and Applications of Hyperbolic Problems, Springer Proceedings in Mathematics & Statistics (PROMS) 236, 2018.
    URL: https://doi.org/10.1007/978-3-319-91545-6
  3. C. Helzel and M. J. Berger, Cartesian grid embedded boundary methods for hyperbolic problems, pp. 675--683, In Hyperbolic Problems: Theory, Numerics, Applications, F.Ancona, A.Bressan, P.Marcati and A.Marson (Eds.), AIMS on Applied Mathematics Vol. 8, 2014.
  4. C. Helzel, J. Kirsten and F. Otto, Suspensions of rod-like molecules: A FV-ELLAM-type discretization of the Smoluchowski equation describing the orientation of rod-like molecules, Eymard, Robert (ed.); H\'erard, Jean-Marc (ed.) Finite volumes for complex applications V, Proceedings of the 5th International Symposium, Aussois, June 2008, pp. 495--502, 2008.
  5. C. Helzel, Simulations of the spurt phenomena for suspensions of rod-like molecules, Bonilla, Luis L. (ed.) et al., Progress in industrial mathematics at ECMI 2006. Papers of the 14th European conference of the European Consortium for Mathematics in Industry, Leganés, Madrid, Spain, July 10--14, 2006. Berlin: Springer. Mathematics in Industry 12, pp. 312-316, 2008.
  6. D. Calhoun, C. Helzel and R. J. LeVeque, A finite volume grid for solving hyperbolic problems on the sphere, Benzoni-Gavage, Sylvie (ed.) et al., Hyperbolic problems. Theory, numerics and applications. Proceedings of the 11th international conference on hyperbolic problems, Ecole Normale Supérieure, Lyon, France, July 17--21, 2006. Berlin: Springer. pp. 355-362, 2008.
    URL: link.springer.com/chapter/10.1007/978-3-540-75712-2_31
  7. C. Helzel,  Accurate methods for hyperbolic problems on embedded boundary grids, Proc. 10th Intl. Conf. on Hyperbolic Problems, Osaka, Japan, September 2004.
  8. C. Helzel, Approximation of hyperbolic equations in complex geometries, Oberwolfach Rep., 1: 941--942, 2004.
  9. M. J. Berger and C. Helzel, Grid aligned $h$-box methods for conservation laws in complex geometries, Herbin, Raphaéle (ed.) et al., Finite volumes for complex applications III. Problems and perspectives. Papers from the 3rd symposium of finite volumes for complex applications, Porquerolles, France, June 24--28, 2002. London: Hermes Penton Science. 277-284, 2002.
  10. D. S. Bale and C. Helzel, Crossflow instabilities in the approximation of detonation waves, Int. Ser. Numer. Math., 140:119-128, 2001.
    URL: link.springer.com/chapter/10.1007/978-3-0348-8370-2_13
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