# 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.
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.
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.
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.
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.