Institut für Geometrie und Praktische Mathematik

Publications:

In Journals:

• A. Bollermann, S. Noelle and M. Lukacova-Medvidova, Finite Volume Evolution Galerkin methods for the shallow water equations with dry beds. IGPM report 305 (2010). Commun. Comput. Phys., 10 (2011), pp. 371-404.
  
  
• Y. Xing, C.-W. Shu, and S. Noelle On the advantage of well-balanced schemes for moving-water equilibria of the shallow water equations. IGPM report 315 (2010), RWTH Aachen University. Journal on Scientific Computing 48 (2011), 339-349.
  
  
• C. Steiner and S. Noelle, Timestep control for weakly instationary flows. IGPM report 295 (2009). In: W. Schröder (ed.) Summary of flow modulation and fluid-structure interaction findings. Notes on Numerical Fluid Mechanics and Multidisciplinary Design 109 (2010), pp. 53-76.
  
  
• C. Steiner, S. Müller and S. Noelle, Adaptive timestep control for instationary solutions of the Euler equations. IGPM report 292 (2009). SIAM Journal on Scientific Computing 32, 1617-1651 (2010).
  
  
• S. Noelle, Y. Xing and C.-W. Shu, High-Order Well-balanced Schemes. in: G. Puppo and G. Russo (eds.) Numerical Methods for Balance Laws. Quaderni di Matematica 24 (2010). pp 1-66.
  
  
• C. Steiner and S. Noelle, On adaptive timestepping for weakly instationary solutions of hyperbolic conservation laws via adjoint error control. International Journal for Numerical Methods in Biomedical Engineering 26 (2010), 790–806. (published online in Comm. Numer. Meth. Eng., October 2008).
  
  
• N. Pankratz, J. Natvig, B. Gjevik and S. Noelle, High-order well-balanced finite-volume schemes for barotropic flows. Development and numerical comparisons., IGPM preprint no. 274, RWTH Aachen University; Ocean Modelling, Vol. 18 (2007), 53-79.
  
  
• S. Noelle, Y. Xing and C.-W. Shu, High Order Well-balanced Finite Volume WENO Schemes for Shallow Water Equation with Moving Water. IGPM preprint no. 270, RWTH Aachen University; Journal of Computational Physics, Vol. 226 (2007), 29-58.
  
  
• M. Lukacova-Medvidova, S. Noelle, M. Kraft, Well-balanced finite volume evolution Galerkin methods for the shallow water equations. , IGPM preprint no. 259, RWTH Aachen University; Journal of Computational Physics, Vol. 221 (2007), 122-147
  
  
• S. Noelle, N. Pankratz, G. Puppo and J. Natvig, Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows., IGPM preprint no. 251, RWTH Aachen University; Journal of Computational Physics, Vol. 213 (2006), 474-499.
  
  
• S. Noelle, W. Rosenbaum, M. Rumpf. 3D Adaptive central schemes: part I. Algorithms for assembling the dual mesh. Applied Numerical Mathematics Vol. 56 (2006), 778-799.
  
  
• S. Noelle, Abelpreis 2005 an Peter D. Lax. DMV Mitteilungen 13 (2005), 84-89.
  
  
• T. Kröger and S. Noelle, Numerical comparison of the Method of Transport to a standard scheme. Computers & Fluids, Vol. 34 (2005), 541-560.
  
  
• T. Kröger and S. Noelle. On the connection between some Riemann-solver free approaches to the approximation of multi-dimensional systems of hyperbolic conservation laws. Math. Model. Numer. Anal., Vol. 38 (2004), 989-1009.
  
  
• N. Gray, Y.-C. Tai, and S. Noelle. Shock waves, dead-zones and particle-free regions in rapid granular free surface flows. J. Fluid Mech. Vol. 491 (2003), 161-181.
  
  
• K.-A. Lie and S. Noelle. On the artificial compression method for second order non-oscillatory central difference schemes for systems of conservation laws. SIAM Journal on Scientific Computing, Vol. 24 (2003), no. 4, 1157-1174.
  
  
• K.-A. Lie and S. Noelle. An improved quadrature rule for the flux-computation in high-resolution non-oscillatory central difference schemes for systems of conservation laws in multidimensions. Journal on Scientific Computing, Vol. 18 (2003), no. 1, 69-81.
  
  
• Y.-C. Tai, S. Noelle, N. Gray and K. Hutter. Shock capturing and front tracking methods for granular avalanches. Journal of Computational Physics, Vol. 175 (2002), 269--301.
  
  
• A. Kurganov, S. Noelle and G. Petrova. Semi-Discrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton-Jacobi Equations. SIAM Journal on Scientific Computing, Vol. 23 (2001), 707--740.
  
  
• S. Noelle. The MoT-ICE: a new high-resolution wave-propagation algorithm for multi-dimensional systems of conservation laws based on Fey's Method of Transport. Journal of Computational Physics, Vol. 164 (2000), 283-334.
  
  
• M. Westdickenberg and S. Noelle. A new convergence proof for finite volume schemes using the kinetic formulation of conservation laws. SIAM Journal on Numerical Analysis, Vol. 37 (2000), 742-757.
  
  
• S. Noelle. Radially symmetric solutions for a class of hyperbolic systems of conservation laws. Zeitschrift für Angewandte Mathematik und Physik (ZAMP), Vol. 48 (1997) 676-679.
  
  
• S. Noelle. A note on entropy inequalities and error estimates for higher order accurate finite volume schemes on irregular families of grids. Mathematics of Computation, Vol. 65 (1996), 1155--1163.
  
  
• S. Noelle. Development of singularities for the complex Burgers equation. Nonlinear Analysis: Theory, Methods, Applications, Vol. 26 (1996), 1313--1321.
  
  
• S. Noelle. Convergence of higher order finite volume schemes on irregular grids. Advances in Computational Mathematics, Vol. 3 (1995), 197--218.
  
  
• D. Kröner, S. Noelle and M. Rokyta. Convergence of higher order upwind finite volume schemes on unstructured grids for scalar conservation laws in several space dimensions. Numerische Mathematik, Vol. 71 (1995), 527--560.
  
  
• S. Noelle. Hyperbolic systems of conservation laws, the Weyl equation, and multidimensional upwinding. Journal of Computational Physics, Vol. 115 (1994), 22--26.
  
  

• M. Castro, J.T. Frings, S. Noelle, C. Pares, G. Puppo On the hyperbolicity of two- and three-layer shallow water equations. Submitted to Proceedings of the 13th International Conference on Hyperbolic Problems (Peking, June 15-19, 2010) (Sept.30, 2010).
  
  
• T. Kröger and S. Noelle. Riemann-solver free schemes. In: Analysis and numerics for conservation laws, 429--451, Springer, Berlin, 2005.
  
  
• S. Noelle, W. Rosenbaum, and M. Rumpf. Multidimensional adaptive staggered grids. In: Analysis and numerics for conservation laws, 479--493, Springer, Berlin, 2005.
  
  
• S. Noelle and M. Westdickenberg. Convergence of Approximate Solutions of Conservation Laws. In: Geometric analysis and nonlinear partial differential equations, 417--430, Springer, Berlin, 2003.
  
  
• K.-A. Lie and S. Noelle. High resolution nonoscillatory central difference schemes for the 2D Euler equations via artificial compression. In: Progress in Industrial Mathematics at ECMI 2000, Eds., M. Anile, V. Capasso, and A. Greco, Mathematics in Industry, Vol. 1, pp. 318-324, Springer Verlag, 2002.
  
  
• K.-A. Lie, S. Noelle and W.Rosenbaum. On the resolution and stability of central difference schemes. In: Finite Volumes for Complex Applications III Problems and Perspektives, edited by Raphaele Herbin, Dietmar Kröner. Hermes Penton Science 2002, 793 -- 800.
  
  
• M. Fey, S. Noelle and C. von Törne. MOTICE: a new multi-dimensional wave-propagation-algorithm based on Fey's Method of Transport. With application to the Euler- and MHD-equations. In: Hyperbolic problems: theory, numerics, applications, Vol. I (Magdeburg, 2000), 373--380. Internat. Ser. Numer. Math. 140, Birkhäuser, Basel, 2001.
  
  
• S. Noelle, W. Rosenbaum and M. Rumpf. An adaptive staggered grid scheme for conservation laws. In: Hyperbolic problems: theory, numerics, applications, Vol. II (Magdeburg, 2000), 775 -- 784. Internat. Ser. Numer. Math. 141, Birkhäuser, Basel, 2001.
  
  
• Y.-C. Tai, S. Noelle, N. Gray and K. Hutter. An accurate shock-capturing finite difference method to solve the Savgae-Hutter equations in avalanche dynamics. In: Proceedings of the International Symposium on Snow, Avalanches and Impact of the Forest Cover, Innsbruck 2000. Annals of Glaciology 32 (2001), 263 -- 267.
  
  
• Y.-C. Tai, N. Gray, K. Hutter and S. Noelle. Flow of dense avalanches past obstructions. In: Proceedings of the International Symposium on Snow, Avalanches and Impact of the Forest Cover, Innsbruck 2000. Annals of Glaciology 32 (2001), 281 -- 284.
  
  
• S. Noelle. Multidimensional flux-vector-splitting and high-resolution characteristic schemes. In: Godunov methods (Oxford, 1999), 671--676, Kluwer/Plenum, New York, 2001.
  
  
• S. Noelle. The MoT-ICE: a new high-resolution wave-propagation algorithm based on Fey's Method of Transport. Invited plenary lecture. In: Proceedings of the Second International Symposium on Finite Volumes for Complex Applications, Duisburg 1999, 95 -- 115 (Hermes).
  
  
• M. Westdickenberg and S. Noelle. A new convergence proof for finite volume schemes. In: Hyperbolic problems: theory, numerics, applications, Vol. II (Zürich, 1998), 983--992, Internat. Ser. Numer. Math., 130, Birkhäuser, Basel, 1999.
  
  
• S. Noelle. A comparison of third and second order accurate finite volume schemes for the two-dimensional compressible Euler equations. In: Hyperbolic problems: theory, numerics, applications, Vol. II (Zürich, 1998), 757--766, Internat. Ser. Numer. Math., 130, Birkhäuser, Basel, 1999.
  
  

• S. Noelle. Zur theoretischen Absicherung moderner numerischer Verfahren für hyperbolische Erhaltungssätze. Öffentliche Antrittsvorlesung an der Mathematisch-Naturwissenschaftlichen Fakultüt der Rheinischen Friedrichs-Wilhelms-Universität Bonn (27. Mai 1998).
  
  
• S. Noelle. On the limits of operator splitting: numerical experiments for the complex Burgers equation. Technical Report TR 91-3, Konrad Zuse-Zentrum Berlin (1991).
  
  

• S. Noelle. High order finite volume schemes for the two-dimensional compressible Euler equations. Habilitationsschrift, Universität Bonn (1997).
  
  
• S. Noelle. Cauchy problems for the complex Burgers equation in one and two space dimensions. Dissertation, Courant Institute, New York University (1990).