List of Publications - Prof. Dr. Christiane Helzel

S.Dahm and J.Giesselmann and C.Helzel: Numerical Discretisation of Hyperbolic Systems of Moment Equations Describing Sedimentation in Suspensions of Rod-Like Particles. (2024)
URL: https://arxiv.org/pdf/2401.14817.pdf

E.Chudzik and C.Helzel and M.Luká\v{c}ová-Medvid'ová: Active Flux Methods for Hyperbolic Systems using the Method of Bicharacteristics. J. Sci. Comput, accepted (2024)

D.Calhoun and E.Chudzik and C.Helzel: The Cartesian Grid Active Flux Method with Adaptive Mesh Refinement. J. Sci. Comput., 94 (2023)
URL: https://link.springer.com/article/10.1007/s10915-023-02106-8

S.Dahm and C.Helzel: Hyperbolic Systems of Moment Equations Describing Sedimentation in Suspensions of Rod-Like Particles. Multiscale Model. Simul., 40 p. 1002-1039 (2022)
URL: https://doi.org/10.1137/21M1464592

E.Chudzik and C.Helzel and D.Kerkmann: The Cartesian Grid Active Flux Method: Linear stability and bound preserving limiting. Applied Mathematics and Computation, 391 (2021)
URL: https://doi.org/10.1016/j.amc.2020.125501

C.Helzel and D.Kerkmann: An active flux method for cut cell grids. In: Finite Volume for Complex Applications IX - Methods, Theoretical Aspects, Examples. Springer International Publishing, Cham, p. 507-515 (2020)
URL: https://link.springer.com/chapter/10.1007/978-3-030-43651-3_47

C.Helzel: A third order accurate wave propagation algorithm for hyperbolic partial differential equations. Communications on Applied Mathematics and Computation, (2020)
URL: https://link.springer.com/article/10.1007/s42967-019-00056-3

C.Helzel and M.Schneiders: Numerical approximation of the Smoluchowski equation using radial basis functions. Journal of Computational Mathematics, 38 p. 176-194 (2020)
URL: https://doc.global-sci.org/uploads/admin/article_pdf/20200224/b9bed8fe162c0390de754f5ce141da34.pdf

C.Helzel and D.Kerkmann and L.Scandurra: A new ADER method inspired by the active flux method. J. Sci. Comput., 80 p. 1463-1497 (2019)
URL: https://doi.org/10.1007/s10915-019-00988-1

P.Buchmüller and J.Dreher and C.Helzel: Improved Accuracy of High-Order WENO Finite Volume Methods on Cartesian Grids with Adaptive Mesh Refinement. In: Theor, Numerics and Applications of Hyperbolic Problems I. Springer International Publishing, Cham, p. 263-272 (2018)
URL: https://doi.org/10.1007/978-3-319-91545-6

C.Helzel and A.E.Tzavaras: A kinetic model for the sedimentation of rod-like particles. Multiscale Model. Simul., p. 500-536 (2017)
URL: http://epubs.siam.org/doi/abs/10.1137/15M1023907

C.Helzel and A.E.Tzavaras: A comparison of macroscopic models describing the collective response of sedimenting rod-like particles in shear flow. Phys. D, 337 p. 18-29 (2016)
URL: http://dx.doi.org/10.1016/j.physd.2016.07.004

P.Buchmüller and J.Dreher and C.Helzel: Finite volume WENO methods for hyperbolic conservation laws on Cartesian grids with adaptive mesh refinement. Applied Mathematics and Computation, p. 460-478 (2016)
URL: http://www.sciencedirect.com/science/article/pii/S0096300315003926

P.Buchmüller and C.Helzel: Improved accuracy of high-order WENO finite volume methods on Cartesian grids. J. Sci. Comput., 61 p. 343-368 (2014)
URL: http://dx.doi.org/10.1007/s10915-014-9825-1

C.Helzel and J.A.Rossmanith and B.Taetz: A high-order unstaggered constrained-transport method for the three-dimensional ideal magnetohydrodynamic equations based on the method of lines. SIAM J. Sci. Comput., 35 p. A623-A651 (2013)
URL: http://dx.doi.org/10.1137/120870323

M.J.Berger and C.Helzel: A simplified h-box method for embedded boundary grids. SIAM J. Sci. Comput., 34 p. A861-A888 (2012)
URL: http://dx.doi.org/10.1137/110829398

C.Helzel and J.A.Rossmanith and B.Taetz: An unstaggered constrained transport method for the 3D ideal magnetohydrodynamic equations. J. Comput. Phys., 230 p. 3803-3829 (2011)
URL: http://dx.doi.org/10.1016/j.jcp.2011.02.009

C.Helzel and R.J.LeVeque: Numerical approximation of stiff reacting flow. In: Numerical methods for balance laws. Vol. 24, (Quad. Mat.), Dept. Math., Seconda Univ. Napoli, Caserta, p. 123-155 (2009)

M.J.Berger and D.A.Calhoun and C.Helzel and R.J.LeVeque: Logically rectangular finite volume methods with adaptive refinement on the sphere. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 367 p. 4483-4496 (2009)
URL: http://dx.doi.org/10.1098/rsta.2009.0168

D.A.Calhoun and C.Helzel: A finite volume method for solving parabolic equations on logically Cartesian curved surface meshes. SIAM J. Sci. Comput., 31 p. 4066-4099 (2009/10)
URL: http://dx.doi.org/10.1137/08073322X

D.Calhoun and C.Helzel and R.J.LeVeque: A finite volume grid for solving hyperbolic problems on the sphere. In: Hyperbolic problems: theory, numerics, applications. Springer, Berlin, p. 355-362 (2008)
URL: http://dx.doi.org/10.1007/978-3-540-75712-2_31

C.Helzel: Simulations of the spurt phenomenon for suspensions of rod-like molecules. In: Progress in industrial mathematics at ECMI 2006. Vol. 12, (Math. Ind.), Springer, Berlin, p. 312-316 (2008)
URL: http://dx.doi.org/10.1007/978-3-540-71992-2_42

C.Helzel and 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. In: Finite volumes for complex applications V. ISTE, London, p. 495-502 (2008)

D.A.Calhoun and C.Helzel and R.J.LeVeque: Logically rectangular grids and finite volume methods for PDEs in circular and spherical domains. SIAM Rev., 50 p. 723-752 (2008)
URL: http://dx.doi.org/10.1137/060664094

C.Helzel: Accurate methods for hyperbolic problems on embedded boundary grids. In: Hyperbolic problems: theory, numerics and applications. {II}. Yokohama Publ., Yokohama, p. 1-8 (2006)

C.Helzel and F.Otto: Multiscale simulations for suspensions of rod-like molecules. J. Comput. Phys., 216 p. 52-75 (2006)
URL: http://dx.doi.org/10.1016/j.jcp.2005.11.028

C.Helzel and M.J.Berger and R.J.LeVeque: A high-resolution rotated grid method for conservation laws with embedded geometries. SIAM J. Sci. Comput., 26 p. 785-809 (electronic) (2005)
URL: http://dx.doi.org/10.1137/S106482750343028X

M.J.Berger and C.Helzel and R.J.LeVeque: h-box methods for the approximation of hyperbolic conservation laws on irregular grids. SIAM J. Numer. Anal., 41 p. 893-918 (2003)
URL: http://dx.doi.org/10.1137/S0036142902405394

M.J.Berger and C.Helzel: Grid aligned h-box methods for conservation laws in complex geometries. In: Finite volumes for complex applications, {III} (Porquerolles, 2002). Hermes Sci. Publ., Paris, p. 263-270 (2002)

D.S.Bale and C.Helzel: Crossflow instabilities in the approximation of detonation waves. In: Hyperbolic problems: theory, numerics, applications, Vol. I, II (Magdeburg, 2000). Vol. 141, (Internat. Ser. Numer. Math., 140), Birkhäuser, Basel, p. 119-128 (2001)

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. Springer, Berlin, p. 775-803 (2001)

C.Helzel and R.J.LeVeque and G.Warnecke: A modified fractional step method for the accurate approximation of detonation waves. SIAM J. Sci. Comput., 22 p. 1489-1510 (2000)
URL: http://dx.doi.org/10.1137/S1064827599357814

C.Helzel and K.Petras: Numerical estimation of projection constants. Numer. Funct. Anal. Optim., 18 p. 555-566 (1997)
URL: http://dx.doi.org/10.1080/01630569708816778