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List of Publications - Prof. Dr. Christiane Helzel

Journal Publications:

1. C. Helzel and K. PetrasNumerical estimation of projection constants, Numer. Funct. Anal. and Optimiz. 18 (5 & 6), 555-566, 1997.
URL: www.tandfonline.com/doi/abs/10.1080/01630569708816778&nbsp;
2. 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: dx.doi.org/10.1137/S1064827599357814
3. 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: dx.doi.org/10.1137/S0036142902405394
4. C. Helzel, M. J. Berger and R. J. LeVequeA high-resolution rotated grid method for conservation laws with embedded geometries, SIAM J. Sci. Comput., 28: 785--809, 2005.
URL: dx.doi.org/10.1137/S106482750343028X
5. 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
6. 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: dx.doi.org/10.1137/060664094
7. 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: dx.doi.org/10.1007/978-3-540-75712-2_31
8. 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: dx.doi.org/10.1098/rsta.2009.0168
9. 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: dx.doi.org/10.1016/j.jcp.2011.02.009
10. M. J. Berger and C. Helzel, A simplified $h$-box method for embedded boundary grids, SIAM J. Sci. Comput., 34: A861--A888, 2012.
URL: dx.doi.org/10.1137/110829398
11. 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: dx.doi.org/10.1137/120870323
12. 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: dx.doi.org/10.1007/s10915-014-9825-1
13. 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: www.sciencedirect.com/science/article/pii/S0096300315003926
14. 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: dx.doi.org/10.1016/j.physd.2016.07.004
15. C. Helzel and A. E. Tzavaras, A kinetic model for the sedimentation of rod-like particles, Multiscale Modelling & Simulation, 15: 500-536, 2017.
URL: epubs.siam.org/doi/abs/10.1137/15M1023907
16. 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: doi.org/10.1007/s10915-019-00988-1
17. C. Helzel and M. SchneidersNumerical approximation of the Smoluchowski equation using radial basis functions, Journal of Computational Mathematics, 38: 176-194, 2020.
URL: doc.global-sci.org/uploads/admin/article_pdf/20200224/b9bed8fe162c0390de754f5ce141da34.pdf
18. 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: link.springer.com/article/10.1007/s42967-019-00056-3
19. 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: www.sciencedirect.com/science/article/pii/S0096300320304598

Book Chapters:

1. 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
2. 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.

Proceedings:

1. 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
2. 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.
3. C. Helzel, Approximation of hyperbolic equations in complex geometries, Oberwolfach Rep., 1: 941--942, 2004.
4. C. Helzel,  Accurate methods for hyperbolic problems on embedded boundary grids, Proc. 10th Intl. Conf. on Hyperbolic Problems, Osaka, Japan, September 2004.
5. 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
6. 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.
7. 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.
8. 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
9. 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: doi.org/10.1007/978-3-319-91545-6
10. 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: link.springer.com/chapter/10.1007/978-3-030-43651-3_47
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