Prof. Dr. Dietmar Kröner

Dietmar Kröner

Department for Applied Mathematics
University of Freiburg
Hermann-Herder-Str. 10, Room 215
79104 Freiburg im Breisgau

Tel: 0761 / 203 5637
E-Mail: dietmar@mathematik.uni-freiburg.de
Office hours: on appointment

Curriculum vitae | Publications | Projects | Presentations, conferences, research stays
Research interests | Working group's main research fields
Teaching | Representative lecturel | Proposed topics for diploma or PhD theses

 

Curriculum vitaePfeil nach unten_geschlossen_003592_transparent.png

Education | Acadamic positions | Awards | Editorial activities | Further activities | Supervised Ph.D. theses and habilitations


born on February 10, 1951 in Lengerich
married, three children

 

Education

Habilitation at the University of Bonn (January, 1986).
Granting of the doctorate by the University of Heidelberg (January, 1982).
Diploma in Mathematics, University of Heidelberg (August, 1977).
Studies in Muenster and Heidelberg (1971-1977).
Military service (1969-1971).


Academic positions

Full professorship (C4) at the Department of Applied Mathematics at the University of Freiburg since 1992.
Professorship (C3) at the Institute of Applied Mathematics and SFB 256 at the University of Bonn (1990–1992).
Scientific assistant at the Institute of Applied Mathematics and SFB 123 at the University of  Heidelberg in 1990.
Assigned chair (C3) at the Institute of Applied Mathematics and SFB 123 at the University of Heidelberg (1989–1990).
Assigned chair at the Institute of Applied Mathematics at the University of Saarbrücken (1988–1989).
Scientific assistant at the Institute of Applied Mathematics at the University of Heidelberg (1986–1988).
Scientific assistant at the Institute of Applied Mathematics at the University of Bonn (1982–1986).
Scientific assistant at the Institute of Applied Mathematics at the University of Bochum (1980-1982).
Scientific assistant at the Institute of Mathematics at the RWTH Aachen (1977-1980).

Moreover, I had been offered two chairs, one at the University of Kaiserslautern, one at the University of Paderborn. Both calls I declined.
 

AwardsPfeil nach unten_geschlossen_003592_transparent.png
Bolzano Prize of the Charles University of Prague for
 
Convergence of upwind finite volume schemes for scalar conservation laws in twodimensions.
SIAM J. Numer. Anal. 31, (2) 324-343 (1994); (in co-operation with M. Rokyta).
 
 

Editorial activities

  • Journal of Mathematical Fluid Mechanics
  • International Journal on Finite Volume Schemes
  • Computational Technologies
  • SIAM Journal of Numerical Analysis (beendet)


Further scientific activities

University of Freiburg:
Member of the Senate (since Fall/Winter 2010).
Vice Dean of the Faculty of Mathematics and Physics (2004-2006).
Managing director of the Institute of Mathematics (2004-2006).
Dean of the Faculty of Mathematics (1995-1997).
 
Deutsche Forschungsgemeinschaft (DFG):
Speaker of the joint DFG–CNRS research group ”Micro-Macro Modelling and Simulation of Liquid-Vapour Flows” (2005-2009).
Coordinator and speaker of the DFG – Graduate School "Non-linear Differential Equations: Modelling, Theory, Numerics, Visualization", Freiburg (1996–2004).
 
Research institutions:Pfeil nach unten_geschlossen_003592_transparent.png
Member of the Peer Review Board of the John von Neumann Institute for Computing (NIC), Jülich (since 2009).
Vice speaker of the research association "Wissenschaftliches Rechnen in Baden-Württemberg" (Scientific Computing in Baden-Württemberg).
Vice speaker of the steering committee of the High Performance Computing Center Stuttgart (HLRS), Stuttgart (since 2007).
Speaker of theScientific Board of the Weierstrass Institute of Applied Analysis and Stochastics (WIAS), Berlin (2004-2007).
Member of the Scientific Board of the Weierstrass Institute of Applied Analysis and Stochastics (WIAS), Berlin (1999-2007).
 
Conferences and congresses:
Member of the Scientific Board of the "International Conference of Hyperbolic Problems: Theory, Numerics, Applications" (Maryland 2008, Beijing 2010, Padua 2012).
Chair of several conferences on "Hyperbolic Systems", "Discontinuous Galerkin Process", and "Phase transition" held at the Mathematisches Forschungsinstitut Oberwolfach.


Supervised Ph.D. theses and habilitations

Ph.D. theses:

M. Wierse (1994), T. Mackeben (1997), A. Koop (1998), B. Schupp (1999),
J. Becker (2000), Th. Gessner (2001), M. Ohlberger (2001), M. Küther (2002),
S. Kermer (2002), A. Dedner (2003), M. Wesenberg (2003), J. Jovanovic (2004),
D. Trescher (2005), Ch. Merkle (2006), D. Diehl (2007), R. Klöfkorn (2009).

Habilitations, and postdoctoral fellows who have been appointed to professorship:

M. Rumpf, W. Dörfler, Ch. Rohde, M. Ohlberger, A. Dedner.

 

 

 

Publications

Journal papers | Conference proceedings  | Oberwolfach Reports | Books | Preprints


Papers in peer-reviewed journals

  1. Chalons, C.; Kröner, D.; Thanh, M. D.: A robust numerical method for approximating solutions of a model of two-phase flows and its properties. Applied Mathematics and Computation 219, No. 1 (15. Sept.), 320–344  (2012). 
  2. Kröner, D.; Thanh, M.D.: Numerical treatment of nonconservative terms in resonant regime for fluid flows in a nozzle with variable cross-section. Computers & Fluids 66 (15. Aug.) 130–139 (2012).
  3. Thanh, M.D.; Kröner, D.; Nam, N. T.: Numerical approximation for a Baer-Nunziato model of two-phase flows. Appl. Num. Math. 61, No. 5, 702-721 (2011).
  4. Hermsdörfer, K.; Kraus, C.; Kröner, D.: Interface conditions for limits of the Navier-Stokes-Korteweg model. Interfaces Free Bound. 13, No. 2, 239-254 (2011).
  5. Jung, N.; Haasdonk, B.; Kröner, D.: Reduced Basis Method for Quadratically Nonlinear Transport Equations. Int. J. Comput. Sci. Math. 2, No. 4, 334–353 (2009).
  6. Dedner, A.; Klöfkorn, R.; Kröner, D.: Efficient higher order methods for convection dominated problems on unstructured grids and applications. In: Proceedings of the International Conference “Computational Technologies and Mathematical Modelling in Science, Engineering and Education, September 10-14, 2008, Almaty, Kazakhstan. Joint issue of Computational Technologies 13 (2008) and Bulletin of Kazakh National University, Series: Mathematics, Mechanics, Informatics. No. 3 (58), Part 1, 25-35 (2008).
  7. Kröner, D.; LeFloch, P. G.; Thanh, M.D.: The minimum entropy principle for compressible fluid flows in a nozzle with discontinuous cross-section. ESAIM, Math. Model. Numer. Anal. 42, No.3, 425-442 (2008).
  8. Bänsch, E.; Goncharova, O.; Koop, A.; Kröner, D.: Modelling and numerical investigation of fluid structure interaction in the problem with elastic surface. Preprint 2006.
  9. Besse, N.; Kröner, D.: Convergence of locally divergence-free discontinuous Galerkin methods for the induction equations of the 2D-MHD system. Math. Model. Numer. Anal. 39, No. 6, 1177-1202 (2005).
  10. Kröner, D.; Thanh, M. D.: Numerical solutions to compressible flows in a nozzle with variable cross-section. SIAM J. Numer. Anal. 43, No. 2, 796-824 (2005).
  11. Klassen, L.; Kröner, D.; Schott, Ph.: Finite volume method on unstructured grids in 3D with applications to the simulation of gravity waves. Meteorology and Atmospheric Physics, 82, No.1-4, 259-270, (2003).
  12. Kröner, D.: Numerics and simulations for convection-dominated problems. Vychisl. Tekhnol. 8, Spec. Iss. 4, 59-71 (2003).
  13. Dörfler, W.; Goncharova, O.; Kröner, D.: Numerical studies for flows with free boundary and dynamic contact angle. Z. Angew. Math. Mech. 82, No.3 (2002), 167-176.
  14. Pfeil nach unten_geschlossen_003592_transparent.pngKlöfkorn, R.; Kröner, D.; Ohlberger, M.: Local adaptive methods for convection dominated problems. International Journal for Numerical Methods in Fluids 40, No.1-2, 79-91 (2002).
  15. Dedner, A.; Kemm, F.; Kröner, D.; Munz, C.-D.; Schnitzer, T.; Wesenberg, M.: Hyperbolic Divergence Cleaning for MHD Equations. Journal of Computational Physics, Vol. 175, No.2, 645-673, (2002).
  16. Haasdonk, B.; Kröner, D.; Rohde, C.: Convergence of a Staggered-Lax-Friedrichs-Scheme on Unstructured Grids in 2D. Numer. Math. 88, No.3, 459-484 (2001).
  17. Dedner, A.; Kröner, D.; Sofronov, I.L.; Wesenberg, M.: Transparent Boundary Conditions for MHD Simulations in Stratified Atmospheres. J. Comput. Phys. 171, No.2, 448-478 (2001).
  18. Kröner, D.; Ohlberger, M.: A posteriori error estimates for upwind finite volume schemes for nonlinear conservation laws in multi dimensions. Math. Comput. 69, No.229, 25-39 (2000).
  19. Kröner, D.; Rokyta, M.; Wierse, M.: A Lax-Wendroff type theorem for upwind finite volume schemes in 2-D. East-West J. Numer. Math. 4, No.4, 279-292 (1996).
  20. Kröner, D.; Zajaczkowski, W. M.: Measure-valued solutions of the Euler equations for ideal compressible polytropic fluids. Math. Methods Appl. Sci. 19, No.3, 235-252 (1996).
  21. Kröner, D.; Noelle, S.; Rokyta, M.: Convergence of higher order upwind finite volume schemes on unstructured grids for scalar conservation laws in several space dimensions. Numer. Math. 71, No.4, 527-560 (1995).
  22. Kröner, D.; Rokyta, M.: Convergence of upwind finite volume schemes for scalar conservation laws in two dimensions. SIAM J. Numer. Anal. 31, No.2, 324-343 (1994).
  23. Gilardi, G.; Kröner, D.: The dam problem in unbounded domains. Ann. Mat. Pura Appl., IV. Ser. 164, 321-364 (1993).
  24. Kröner, D.: Absorbing boundary conditions for the linearized Euler equations in 2-D. Math. Comput. 57, No.195, 153-167 (1991).
  25. Kenmochi, N.; Kröner, D.; Kubo, M. Periodic solutions to porous media equations of parabolicelliptic type. J. Partial Differ. Equations 3, No.3, 63-77 (1990).
  26. Pfeil nach unten_geschlossen_003592_transparent.pngKröner, D.: The flow of a fluid with a free boundary and dynamic contact angle. Z. Angew. Math. Mech. 67, No.5, T 304-T 306 (1987).
  27. Kröner, D.: Asymptotische Entwicklungen für Strömungen von Flüssigkeiten mit freiem Rand und dynamischem Kontaktwinkel. (Asymptotic expansions for flows with free boundaries and dynamical contact angle). Preprint, Sonderforschungsbereich 72, Approximation und Optimierung, Univ. Bonn, 809. Bonn: Univ., Habil.-Schr. 105 S. (1986).
  28. Kröner, D. The regularity of the free boundary for a non-steady filtration problem in the case of a compressible flow. Boll. Unione Mat. Ital., VI. Ser., B 5, 881-906 (1986).
  29. Kröner, D.: Asymptotic behaviour of the solution of the non-steady dam problem for incompressible fluids.
    Control Cybern. 14, 247-273 (1985).
  30. Kröner, D.; Rodriques, J.-F.: Global behaviour for bounded solutions of a porous media equation of elliptic-parabolic type. J. Math. Pures Appl., IX. Sr. 64, 105-120 (1985).
  31. Kröner, D.: Regularität der Sickerlinie bei einem instationären Grundwasserproblem (Regularity of the seepage line in a nonstationary groundwaterproblem). Z. Angew. Math. Mech. 64, No.5, T 292-T 294 (1984).
  32. Kröner, D. Parabolic regularization and behaviour of the free boundary for unsaturated flow in a porous medium. J. Reine Angew. Math. 348, 180-196 (1984).
  33. Kröner, D.; Luckhaus, S.: Flow of oil and water in a porous medium. J. Differ. Equations 55, 276-288 (1984).
  34. Kröner, D.: Asymptotic expansions of the pressure and the free boundary for flows through porous media.Manuscr. Math. 44, 131-153 (1983).

 

Peer-reviewed conference proceedings 

  1. Bastian, P.; Berninger, H.; Dedner, A.; Engwer, Chr.; Henning, P.; Kornhuber, R.;Kröner, D.; Ohlberger, M.; Sander, O.; Schiffler, G.; Shokina, N.; Smetana, K.: Adaptive Modelling of Coupled Hydrological Processes with Application in Water Management. In: Günther, M.; Bartel, A.; Brunk, M.; Schöps, S.; Striebel, M. (Eds.): Progress in Industrial Mathematics at ECMI 2010. Proceedings of the 16th European conference on mathematics for industry, Wuppertal, Germany, July 26-30, 2010. Heidelberg : Springer (2012) = Mathematics in Industry 17, Part 6, 561-567 (2012).
  2. Kroener, D.; Mueller, T.: Related Problems for TV-Estimates for Conservation Laws on Surfaces. In: Tatsien Li; Song Jiang (eds.): Hyperbolic Problems. Theory, Numerics and Applications (= Submitted to Proceedings of the 13th International Conference on Hyperbolic Problems, June 15-19, 2010, Peking), Vol.2 , Beijing : Higher Education Press, 584-592 (2012).
  3. Kroener, D.: Jump conditions across phase boundaries for the Navier-Stokes-Korteweg equation. In: Tatsien Li; Song Jiang (eds.): Hyperbolic Problems. Theory, Numerics and Applications (=  Submitted to Proceedings of the 13th International Conference on Hyperbolic Problems, June 15-19, 2010, Peking), Vol.2 , Beijing : Higher Education Press,  494-501 (2012).
  4. Brdar, S.; Dedner, A.; Klöfkorn, R.; Kränkel, M.; Kröner, D.: Simulation of geophysical problems with DUNE-FEM. In: Krause, E.; Kröner, D.; Resch, M.; Shokina, N.; Shokin, Y. (eds.): Computational Science and High Performance Computing IV, The 4th Russian-German Advanced research Workshop, Freiburg, Germany, October 12-16, 2009.  = Notes Numer. Fluid Mech. Multidiscip. Des. (NNFM), Vol. 115, Berlin, Heidelberg : Springer, 93–106 (2011).
  5. Dedner, A.; Kröner, D.; Shokina, N.: Adaptive modelling of two-dimensional shallow water flows with wetting and drying. In: Krause, E.; Kröner, D.; Resch, M.; Shokina, N.; Shokin, Y. (eds.): Computational Science and High Performance Computing IV, The 4th Russian-German Advanced research Workshop, Freiburg, Germany, October 12 to 16, 2009. = Notes on Numerical Fluid Mechanics and Multidisciplinary design (NNFM), Vol 115. Berlin, Heidelberg : Springer, 1-15 (2011).
  6. Dedner, A.; Klöfkorn, R.; Kröner, D.: Higher order adaptive and parallel simulations including dynamic load balancing with the software package DUNE. In: Nagel, W.E.; Kröner; D., Resch, M. (eds.), High Performance Computing in Science and Engineering ’09. Transaction of the High Performance Computing Center Stuutgart (HLRS). Heidelberg: Springer, 229-239 (2010).
  7. Nolte, M.; Kröner, D.: Computing the Effective Hamiltonian for a Time-Dependent Hamiltonian. In: Tadmor, Eitan; Pugh, Mary; Ryzhik, Lenya (eds.), Hyperbolic problems. Theory, numerics and applications. Proceedings of the 12th international conference on hyperbolic problems, June 9–13, 2008, Center for Scientific Computation and Mathematical Modelling, University of Maryland, College Park. Bd. 2: Contributed talks.  = Proceedings of Symposia in Applied Mathematics 67, Part 2, 815–824 (2009).
  8. Klöfkorn, R.; Kröner, D.; Ohlberger, M.: Parallel Adaptive Simulation of PEM Fuel Cells. In: W. Jäger; Krebs, H.J., (eds.), Mathematics. Key Technology for the Future. Joint Projects between Universities and Industry 2004 – 2007, Berlin: Springer, 235-252 (2008).
  9. Bänsch, E.; Goncharova, O.; Koop, A.; Kröner, D.: Mathematical and Numerical Modelling of Fluid Flow in Elastic Tubes. In: E. Krause; Shokin, Y.; Resch, M.; Shokina, N. (eds.), Computational Science and High Performance Computing. The 3rd Russian-German advanced research workshop, Novosibirsk, Russia, July 23 to July 27, 2007. Berlin: Springer (2008) = Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM) 101, 102-121 (2008).
  10. Klöfkorn, R.; Kröner, D.; Ohlberger, M.: Parallel and Adaptive Simulation of Fuel Cells in 3D. In: E. Krause; Shokin, Y.; Resch, M.; Shokina, N. (eds.), Computational Science and High Performance Computing. The 3rd Russian-German advanced research workshop, Novosibirsk, Russia, July 23 to July 27, 2007. Berlin: Springer (2008) = Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM) 101, 69-81 (2008).
  11. Kröner, D.; Thanh, M.D.: On the model of compressible flows in a nozzle mathematical analysis and numerical methods. In: Asakura, F.; H. Aiso, H.; Kawashima, S.; Matsumura, A.; Nishibata, S.; Nishihara, K. (eds.), Hyperbolic problems. Theory, numerics and applications. II. Proceedings of the 10th international conference, Osaka, Japan, September 13–17, 2004. Yokohama: Yokohama Publishers, 117-124 (2006).
  12. Nolte, M.; Kröner, D.: Convergence of well-balanced schemes for the initial boundary value problem for scalar conservation laws in 1D. In: Benzoni-Gavage, S. (ed.); Serre, D. (ed.), Hyperbolic problems. Theory, numerics and applications. Proceedings of the 11th International Conference on Hyperbolic Problems held in Ecole Normale Suprieure, Lyon, France, July 17–21, 2006. Berlin: Springer, 791-798 (2008).
  13. Kröner, D.: Numerics and simulations for convection dominated problems. In: Krause, E. (ed.); Shokin, Y, (ed.); Resch, M. (ed.); Shokina, N. (ed.), Computational science and high performance computing. Russian-German advanced research workshop, Novosibirsk, Russia, September 30 to October 2, 2003. Berlin: Springer (2005) = Notes Numer. Fluid Mech. (NNFM) 88, 367-380 (2005).
  14. Dedner, A.; Kröner, D.; Rohde, C.; Wesenberg, M.: Radiation Magnetohydrodynamics: Analysis for Model Problems and Efficient 3d-Simulations for the Full System. In: Warnecke, G. (ed.), Analysis and Numerics for Conservation Laws. Berlin: Springer, 163-202 (2005).
  15. Klassen, L.; Klimmeck, A.; Kröner, D.; Trescher, D.: Numerical optimisation of scavenging in two-stroke engines with transfer ducts, an exhaust port and moving piston. In: Jäger, W.; Krebs, H.-J. (eds.), Mathematics. Key Technology for the Future. Joint Projects between Universities and Industry. Berlin (u.a.) : Springer, 22-32, (2003).
  16. Dedner, A.; Kröner, D.; Rohde, C.; Schnitzer, T.; Wesenberg, M.: Comparison of Finite Volume and Discontinuous Galerkin Methods of Higher Order for Systems of Conservation Laws in Multiple Space Dimensions. In: Hildebrandt, S. (ed.); Karcher, H. (ed.), Geometric analysis and nonlinear partial differential equations. Berlin : Springer, 573-589 (2003).
  17. Dedner, A.; Kröner, D.; Rohde, C.; Wesenberg, M.: Efficient divergence cleaning in threedimensional MHD simulations. In: Krause, E. (ed.); Jäger, W. (ed.), High perfomance computing in science and engineering ’02. Transactions of the High Perfomance Computing Center Stuttgart (HLRS) 2002. 5th results and review workshop on High Performance Computing in Science and Engineering, Stuttgart, Germany, September 30 - October 1, 2002. Berlin : Springer, 323-334 (2003).
  18. Kröner, D.; Küther, M.; Ohlberger, M.; Rohde, C.: A posteriori error estimates and adaptive methods for hyperbolic and convection dominated parabolic conservation laws. In: Kirkilionis, M.; Krömker, S.; Rannacher, R.; Tomi, F. (eds.): Trends in Nonlinear Analysis. Berlin (u.a.) : Springer, 289 - 306 (2003).
  19. Gessner, T.; Kröner, D.: Godunov Type Methods on Unstructured Grids and Local Mesh Refinement. In: Toro, E.F. (ed.): Godunov methods, theory and applications. (Proceedings of an International Conference on Godunov Methods: theory and applications, held October 18 - 22, 1999, in Oxford, UK.). New York (u.a.) : Kluwer Academic/Plenum Publ., 527-48. (2001).
  20. Dedner, A.; Kröner, D.; Sofronov I.L.; Wesenberg, M.: Absorbing Boundary Conditions for Astrophysical MHD Simulations. In: Toro, E.F. (ed.), Godunov methods, theory and applications. (Proceedings of an International Conference on Godunov Methods: theory and applications, held October 18 - 22, 1999, in Oxford, UK.). New York (u.a.) : Kluwer Academic/Plenum Publ., 217-224. (2001).
  21. Dedner, A.; Kröner, D.; Rohde, C.; Wesenberg, M.: Godunov-type schemes for the MHD equations. In: Toro, E.F. (ed.), Godunov methods, theory and applications. (Proceedings of an International Conference on Godunov Methods: theory and applications, held October 18 - 22, 1999, in Oxford, UK.). New York (u.a.) : Kluwer Academic/Plenum Publ., 209-216. (2001).
  22. Dedner, A., Kröner, D., Rohde, C., Wesenberg, M.: MHD Instabilities Arising in Solar Physics: A Numerical Approach. In: Freistühler, H. (ed.); Warncke, G. (ed.), Hyperbolic problems. Theory, numerics, applications. (Eighth International Conference on Hyperbolic Problems - Theory, Numerics, Applications in Magdeburg, Germany, February/March 2000). Basel (u.a.) : Birkhäuser, 277-286 (2001).
  23. Wierse, M.; Kröner, D.; Müller, A.; Schupp, B.; Schwörer, R.: Simulation of a 3-D piston driven flow. In: Friedrich, R. (ed.); Bontoux, P. (ed.), Computation and visualization of three-dimensional vortical and turbulent flows. Proceedings of the 5th CNRS-DFG workshop on Numerical flow simulation, München, Germany, December 6-7, 1996. Wiesbaden: Vieweg (1998) = Notes Numer. Fluid Mech. 64, 333-349 (1998). 
  24. Kröner, D.: Finite volume schemes in multidimensions. In: Griffiths, D. F. (ed.); Higham, D. J. (ed.); Watson, G.A. (ed.), Numerical analysis 1997. Proceedings of the 17th Dundee biennial conference, University of Dundee, Great Britain, June 24–27, 1997. Harlow: Longman, Scientific & Techn. (1998) = Pitman Res. Notes Math. Ser. 380, 179-192 (1998).
  25. Kröner, D.; Koop, A.; Schupp, B.; Müller, S.; Schmitz, S.; Schroeter, B.: Deformation of an elastic cylindrical tube. (Deformation einer elastischen Flexlippe.) In: Hoffmann, K.-H. (ed.); Jäger, W. (ed.); Lohmann, T. (ed.); Schunck, H. (ed.), Mathematik Schlüsseltechnologie für die Zukunft. Verbundprojekte zwischen Universität und Industrie. Berlin u.a. : Springer. 177-189 (1997).
  26. Wierse, M.; Kröner, D.: Higher order upwind schemes on unstructured grids for the nonstationary compressible Navier-Stokes equations in complex time-dependent geometries in 3D. In: Hirschel, E.-H. (ed.), Flow simulation with high-performance computers II. DFG priority research programme results 1993 - 1995. Wiesbaden: Vieweg (1996) = Notes Numer. Fluid Mech. 52, 369-384 (1996).
  27. Kröner, D.: Finite volume methods in fluid mechanics. In: Galdi, G. P. (ed.); Málek, J. (ed.); Nečas, J. (ed.), Progress in theoretical and computational fluid mechanics. 3rd Winter School, Paseky, Czech Republic, December 12-18, 1993. Harlow, Essex: Longman Scientific & Technical (1994) = Pitman Res. Notes Math. Ser. 308, 73-127 (1994).
  28. Beinert, R.; Kröner, D.: Finite volume methods with local mesh alignment in 2-D. In: Hackbusch, W. (ed.); Wittum, G. (ed.), Adaptive Methods - Algorithms, Theory and Applications. Proceedings of the 9th GAMM-Seminar Kiel, Germany, January 22-24, 1993. Braunschweig: Vieweg (1994) = Notes Numer. Fluid Mech. (NNFM) 46, 38-53 (1994).
  29. Kröner, D.: Finite volume methods for conservation laws. In: Feng, K. (ed.); Shi, Zhong-Ci (ed.), The computation of differential equations and dynamical systems. Proceedings of the international conference held at Beijing, P. R. China, September 1–5, 1992. Singapore: World Scientific (1993) = Ser. Appl. Math. 4, 11-25 (1993).
  30. Kröner, D.: Boundary conditions for the numerical simulation of the initial value problem for the Euler equations on a finite domain. In: Engquist, B. (ed.): Third International Conference on Hyperbolic Problems. Theory, numerical methods and applications. Poceedings. Uppsala, Sweden, June 11-15, 1990, Vol. II, 684-697 (1991).
  31. Kröner, D.: Asymptotic expansions for a flow with a dynamic contact angle. In: Heywood, J. G. (ed.), The Navier-Stokes equations theory and numerical methods. Proceedings of a conference held at Oberwolfach, FRG, Sept. 18-24, 1988. Berlin [u. a.] : Springer (1990) =  Lecture notes in mathematics 1431, 49-59 (1990).
  32. Kröner, D.: Numerical schemes for the Euler equations in two space dimensions without dimensional splitting. In: Ballmann, J. (ed.): Nonlinear hyperbolic equations theory, computation methods, and applications. Proceedings of the Second International Conference on Nonlinear Hyperbolic Problems, Aachen, FRG, March 14 to 18, 1988 = Notes Numer. Fluid Mech. (NNFM) 24, 342-452 (1989).
  33. Kröner, D.: Directionally adapted upwind schemes in 2-D for the Euler equations. In: Hirschel, E. H. (ed.), Finite approximations in fluid mechanics. DFG priority program results 1986-88. Vol. II. Braunschweig u.a. : Vieweg (1989) =  Notes on Numerical Fluid Mechanics and Multidisciplinary design (NNFM) 25, 249-263 (1989).
  34. Kröner, D.: Global behaviour of the solution to the nonsteady filtration problem. In: Bossavit, A. (ed.), Free boundary problems in fluid flow with applications. Proceedings of the International Colloquium 'Free Boundary Problems: Theory and Applications' in Maubuisson/France 1984, Vol. III. Boston : Pitman (1985) = Res. Notes Math. 120, 272-286 (1985).

 

Oberwolfach Reports

  1. Dafermos, C. M.; Kröner, D.; Leveque, R. J.: Hyperbolic Conservation Laws. In: Abstracts from the Workshop held December 7th–December 13th, 2008. Oberwolfach Rep. 5, No. 4, 3139-3200 (2008).
  2. Colombo, R. M.; Kröner, D.; Lefloch,P. G.: Mini-workshop Hyperbolic Aspects of Phase Transition Dynamics. In: Abstracts from the Mini-Workshop held February 24–March 1, 2008. Oberwolfach Rep. 5, No. 1, 513-556 (2008).
  3. Dafermos, C. M.; Kröner, D.; Leveque, R. J.: Hyperbolic Conservation Laws. In: Abstracts from the Workshop held December 7th–December 13th, 2008. Oberwolfach Rep. 1, No. 2, 915–962 (2004).


Books (author or editor)

  1. Krause, E.; Kröner, D.; Resch, M.; Shokina, N.; Shokin, Y. (eds.): Computational Science and High Performance Computing IV, The 4th Russian-German Advanced research Workshop, Freiburg, Germany, October 12 to 16, 2009. Notes on Numerical Fluid Mechanics and Multidisciplinary design (NNFM), Vol 115. Berlin, Heidelberg : Springer 2011.   (contents)
  2. Nagel, W. E. (ed.); Kröner, D. B. (ed.); Resch, M. M. (ed.): High Performance Computing in Science and Engineering '10. Transactions of the High Performance Computing Center, Stuttgart (HLRS) 2010. Berlin : Springer 2010.   (contents - download)
  3. Nagel, W. E. (ed.); Kröner, D. B. (ed.); Resch, M. M. (ed.): High Performance Computing in Science and Engineering ’09. Transactions of the High Performance Computing Center, Stuttgart (HLRS) (2009). Berlin u.a. : Springer 2010.   (contents)
  4. Nagel, W. E. (ed.); Kröner, D. B. (ed.); Resch, M. M. (ed.): High Performance Computing in Science and Engineering ’08. Transactions of the High Performance Computing Center, Stuttgart (HLRS) 2008. Berlin, Heidelberg : Springer 2009.   (contents)
  5. Nagel, W. E. (ed.); Kröner, D. B. (ed.); Resch, M. M. (ed.): High Performance Computing in Science and Engineering ’07. Transactions of the High Performance Computing Center, Stuttgart (HLRS) (2007). Papers presented at 10th Results and Review workshop, Stuttgart, Germany, October 4–5, 2007. Berlin, Heidelberg : Springer 2009.   (contents)
  6. Herbin, D. (ed.); Kröner, D. (ed.): Finite Volumes for Complex Applications III. Problems and Perspectives. Paris : Hermes Science Publ. 2002. (contents of the reprint - download)
  7. Kröner, D. (ed.); Ohlberger, M. (ed.); Rohde, C. (ed.): An Introduction to Recent Developments in Theory and Numerics for Conservation Laws. Proceedings of the International School, Freiburg/ Littenweiler, Germany, October 20–24, 1997. Lecture Notes in Computational Science and Engineering, 5. Berlin, Heidelberg (u.a.) : Springer 1999.   (contents - download)
  8. Kröner, D.: Numerical schemes for conservation laws. Wiley-Teubner Series Advances in Numerical Mathematics. Chichester u.a. : Wiley-Teubner 1997.   (contents - download)
  9. Borchers, W. (ed.); Domick, G. (ed.); Kröner, D. (ed.); Rautmann, R. (ed.); Saupe, D. (ed.): Visualization Methods in High Performance Computing and Flow Simulation. Proceedings of the International Workshop on Visualization, Paderborn, Germany, 18–21 January 1994. Utrecht : VSP, Vilnius : TEV 1996.   (contents)
 

Preprints

  1. Dziuk, G.; Kröner, D.; Müller, T.: Scalar conservation laws on moving hypersurfaces, Preprint, Freiburg 2012.
 
 

Funded projects

 
DFG Schwerpunktprogramm "MetStroem" (SPP 1276)
Project: "Skalenuebergreifende Modellierung in der Stroemungsmechanik und Meteorologie”
Term: since 2007 for a period of 24 months + additional funding for 24 months (Az: De 1509/1-1; Az: De 1509/1-2)
(in co-operation with A. Dedner)
Co-workers: Slavko Brdar; Nina Shokina
Laufzeit: since 2011 for a period of 24 months (GZ: KR 795/20-3)
Co-worker: Slavko Brdar
 
BMBF Verbundprojekt "AdaptHydroMod: Adaptive Modellierung gekoppelter hydrologischer Prozesse mit Anwendungen in der Wasserwirtschaft"
Sub-project: ”Adaptive Modellierung von Oberflaechengewaessern” (AZ: 03DEPAF3) (gemeinsam mit A. Dedner)
Term: since July 1 2007 for a period of 36 months; completed.
Co-worker: Nina Shokina
 
BMBF/BMWi Verbundprojekt "Weiterentwicklung der Rechenprogramme d3f und r3f. Entwicklung Effizienter Diskretisierungsverfahren für die zu entwickelnden numerischen Verfahren zur Datenanalyse"
(Az: 02E10306)
Term: since October 1 2006 of 36 months; completed.
Co-worker: Mirko Kränkel
 
Landesstiftung Baden-Wuerttemberg - Foerderprogramm "High Performance Computing"
Project: ”Simulation des Spuelvorgangs eines Zweitaktmotors unter Beruecksichtigung detaillierter chemischer Verbrennungsprozesse” (in co-operation with D. Lebiedz)
Term: since 2009 for a period of 36 months, until Dec 31 2012
Co-worker: Robert Klöfkorn; currently: Tobias Malkmus
 
DFG-SFB Transregio 71 Geometric Partial Differential Equations (Sonderforschungsbereich)
Project: "C.1 Dynamics on and of surfaces" (in co-operation with G. Dziuk)
Term: since 2009
Co-worker: Thomas Müller
 
DFG-SFB Transregio 71 Geometric Partial Differential Equations (Sonderforschungsbereich)
Project: "C.2 Fluid structure interaction" (in co-operation with M. Růžička)
Term: since 2009
Co-worker: Ioannis Toulopoulos
 
DFG Einzelprojekt ”Compressible phasefield models for phase transition”
Term: since 2009 for a period of 36 months
Co-worker: Mirko Kränkel
 

 

 

Presentations, conference contributions, research staysPfeil nach unten_geschlossen_003592_transparent.png

  • Summer school Bangalore 7/2005
  • Research stay at the Mittag-Leffler-Institut, Schweden 9/2005
  • Hyperbolic Systems Lyon 7/2006
  • Summer school Cargese 8/2006
  • Workshop Heraklion 9/2006
  • Workshop Banff, Canada 10/2006
  • Presentation Banja Luka 12/2006
  • Research stay in Prag 3/2007
  • Presentation Aachen 5/2007
  • Conference Vancouver 8/2007
  • ENUMATH Graz 9/2007
  • Conference Hangzhou, China 10/2007
  • Presentation Karlsruhe 12/2007
  • Workshop Straßburg 1/2008
  • Miniworkshop Oberwolfach 2/2008
  • Conference Calais 3/2008
  • Conference St. Petersburg 5/2008
  • Hyperbolic Systems in Maryland 6/2008
  • Heidelberg 7/2008
  • Conference Almati 9/2008
  • Conference Novosibirsk 10/2008
  • Berlin 10/2008
  • Presentation Bayreuth 11/2008
  • Conference Oberwolfach 12/2008
  • Workshop Aachen 2/2009
  • Workshop Stuttgart 2/2009
  • Presentation Stuttgart 2/2009
  • DFG-CNRS Workshop Freiburg 3/2009
  • DMV 9/2009
  • Conference Heidelberg 10/2009
  • German-Russian Workshop Freiburg 10/2009
  • Berlin 10/2009
  • Frankfurt 10/2009
  • Paris 11/2009
  • Prag 12/2009
  • Jülich 2/2010
  • Straßburg 4/2010
  • Leipzig 4/2010
  • Hefei (China) 6/2010
  • Hyperbolic Systems Conference Peking 6/2010
  • St. Petersburg 9/2010
  • Prag 10/2010

 

 

 

Main research interestsPfeil nach unten_geschlossen_003592_transparent.png

 
  • Numerics for partial differential equations, particularly coonservation equations
  • Numerical fluid mechanics
  • Free boundary value problems
  • Scientific computing

 

 

Proposed topics for diploma or PhD thesesPfeil nach ganz oben_geschlossen_afafaf_transparent.png

 
for Diploma theses
  • Transparente Randbedingungen und Hybrid-Gitter
  • Entwicklung eines effizienten Verfahrens zur Lösung hyperbolischer Differentialgleichungen
  • Erweiterung eines Programms für reaktive Stroemungen um Reibungsterme.
  • Lokale Existenz für ein System von Gleichungen zur Beschreibung von Elektrolyt-Polymer-Gele
 
for PhD theses