Volker Elling

I am an Associate Professor in the Mathematics Department at University of Michigan. I work on hyperbolic systems of conservation laws, with focus on self-similar solutions and mixed-type and degenerate problems.

My email: velling@umich.edu
Office: East Hall 2856

Grants

Sloan Research Fellowship (2011-2013)

Rackham Spring/Summer Research Grant (summer 2010)

Rackham Faculty Research Grant (2010/11)

NSF DMS-0904074 (2009-2012)

Publications

In scientific journals:

• Realizing distributed computational laboratories
  Beth Plale, Volker Elling, Greg Eisenhauer, Karsten Schwan, Davis King, Vernard Martin
  Int. J. of Parallel and Distributed Systems and Networks, Vol 2., No. 3, 1999
   
• A possible counterexample to wellposedness of entropy solutions and to Godunov scheme convergence
  Volker Elling
  Preprint arXiv:math.NA/0509333 (older versions: Technical report SCCM-03-05, SCCM Program, Stanford University, 2003)
  Mathematics of Computation, Vol. 75 no. 256 (2006), p. 1721-1733
   
• A Lax-Wendroff type theorem for unstructured quasiuniform grids
  Volker Elling
  Preprint arXiv:math.NA/0509331 (older versions: Technical report SCCM-03-07, SCCM Program, Stanford University, 2003)
  Mathematics of Computation, vol. 76, no. 257 (2007), p. 251-272
   
• The ellipticity principle for selfsimilar polytropic potential flow
  Volker Elling, Tai-Ping Liu
  Preprint arXiv:math.AP/0509332 (older versions: Technical report SCCM-04-01, SCCM Program, Stanford University, 2004)
  Journal of Hyperbolic Differential Equations, Vol. 2, No. 4 (December 2005), p. 909-917
   
• The carbuncle phenomenon is incurable
  Volker Elling
  Acta Math. Sci. (ser. B) vol. 29 no. 6 (2009), p. 1647-1656
   
• Supersonic flow onto a solid wedge
  Volker Elling and Tai-Ping Liu
  Preprint arXiv:0707.2108 [math-ph]
  Communications on Pure and Applied Mathematics, vol. 61 no. 10 (Oct. 2008), p. 1347-1448
   
• Regular reflection in self-similar potential flow and the sonic criterion
  Volker Elling
  Preprint arXiv:0710.0104 [math-ph]
  Commun. Math. Anal., vol. 8 no. 2 (2010), p. 22-69
   
• Counterexamples to the sonic criterion
  Volker Elling
  Preprint arXiv:0810.2137 [math-ph]
  Arch. Rat. Mech. Anal., vol. 195 no. 3 (Dec. 2009), p. 987-1010
   
• Instability of strong regular reflection and counterexamples to the detachment criterion
  Volker Elling
  Preprint arXiv:0908.0106 [math-ph]
  SIAM J. Appl. Math., vol. 70 no. 4 (2009), p. 1330-1340
   
• Hölder continuity and differentiability on converging subsequences
  Volker Elling
  Accepted by Acta Math. Sci.
   
• Non-existence of strong regular reflections in self-similar potential flow
  Volker Elling
  Preprint arXiv:1104.0330
  Accepted by J. Diff. Eqns.
   
• Existence of multi-branched algebraic vortex spirals
  Volker Elling
  submitted
   
• Steady self-similar inviscid flow
  Volker Elling and Joseph Roberts
  Preprint arXiv:1104.0331
  submitted
   

Other scientific publications:

• A spectral method for mapping dataflow graphs
  Volker Elling
  Master's Thesis, Georgia Institute of Technology, 1998
   
• Min-cut methods for mapping dataflow graphs
  Volker Elling, Karsten Schwan
  In: Proceedings of Euro-Par '99, pages 203-212, Lecture Notes in Computer Science 1685, Springer 1999
   
• Numerical simulation of gas flow in moving domains
  Volker Elling
  Diploma thesis, RWTH Aachen, Germany, 2000
   
• A Lax-Wendroff type theorem for unstructured grids
  Volker Elling
  Ph.D. dissertation, SCCM Program, Stanford University, 2004
   
• Carbuncles as similar entropy solutions
  Volker Elling
  Preprint arXiv:math.AP/0609666
   
• Nonuniqueness of entropy solutions and the carbuncle phenomenon
  Volker Elling
  Hyperbolic Problems. Theory, Numerics and Applications. (Proceedings of the 10th Conference on Hyperbolic Problems (HYP2004), Osaka, Japan, September 13-17, 2004). Vol. I, p. 375-382
   
• Physicality of Weak Prandtl-Meyer Reflection
  Volker Elling, Tai-Ping Liu
  Mathematical Analysis in Fluid and Gas Dynamics. (RIMS Kokyuroku no. 1495, May 2006, Research Institute for Mathematical Sciences, Kyoto University.) Pages 112-117.
   
• Exact solutions to supersonic flow onto a solid wedge
  Volker Elling, Tai-Ping Liu
  Hyperbolic Problems. Theory, Numerics, Applications. (Proceedings of the 11th Conference on Hyperbolic Problems (HYP2006), Lyon, France, July 17-21, 2006), p. 101-112
   
• Counterexamples to the sonic and detachment criteria
  Volker Elling
  Hyperbolic Problems. Theory, Numerics, Applications. (Proceedings of the 12th Conference on Hyperbolic Problems (HYP2008), College Park, MD, USA, June 2008)