Prof. Dr. Dietmar Kröner

Abteilung für Angewandte Mathematik
Albert-Ludwigs-Universität Freiburg
Hermann-Herder-Str. 10

79104 Freiburg i. Br.

Tel.: 0761/203-5637
privat: 07822/5830
Fax: 0761/203-5632

Zur Person | Publikationen | Drittmittelprojekte | Vorträge, Forschungsaufenthalte, Tagungen
Forschungsinteressen | Forschungsschwerpunkte der Arbeitsgruppe
Lehrveranstaltungen | Skripte | Vorlesungsbeispiel | Vorschläge für Diplomarbeiten und Dissertationen

Zur Person

Ausbildung | Akad. Werdegang | Preise | Herausgeberschaft | weitere Aktivitäten | betr. Dissertationen und Habilitationen

geboren am 10. Februar 1951 in Lengerich
verheiratet, drei Kinder

Ausbildung

Militärdienst (1969-1971).
Studium in Münster und Heidelberg (1971-1977).
Diplom in Mathematik an der Universität Heidelberg (August 1977).
Promotion an der Universität Heidelberg (Januar 1982).
Habilitation an der Universität Bonn (Januar 1986).

Akademischer Werdegang

Wissenschaftlicher Angestellter am Mathematischen Institut der RWTH Aachen (1977-1980).
Wissenschaftlicher Angestellter am Mathematischen Institut der Universität Bochum (1980-1982).
Wissenschaftlicher Angestellter am Institut für Angewandte Mathematik an der Universität Bonn (1982–1986).
Wissenschaftlicher Angestellter am Institut für Angewandte Mathematik an der Universität Heidelberg (1986–1988).
Lehrstuhlvertretung am Institut für Angewandte Mathematik an der Universität Saarbrücken (1988–1989).
Lehrstuhlvertretung (C3) am Institut für Angewandte Mathematik und SFB 123 an der Universität Heidelberg (1989–1990).
Wissenschaftlicher Angestellter am Institut für Angewandte Mathematik und SFB 123 an der Universität Heidelberg 1990.
Professur (C3) am Institut für Angewandte Mathematik und SFB 256 an der Universität Bonn (1990–1992).
Professur (C4) am Institut für Angewandte Mathematik an der Universität Freiburg seit 1992.

Weitere Rufe auf Professuren (C4) erfolgten an die Universitäten Kaiserslautern und Paderborn und wurden von mir abgelehnt.

Preise

Bolzano-Preis der Karls-Universität Prag für

Convergence of upwind finite volume schemes for scalar conservation laws in twodimensions.
SIAM J. Numer. Anal. 31, (2) 324-343 (1994).

in Zusammenarbeit mit M. Rokyta.

Mitherausgeber der Zeitschriften

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

Weitere Aktivitäten

Universität Freiburg:

Deutsche Forschungsgemeinschaft (DFG):

Wissenschaftliche Einrichtungen:

Tagungen und Kongresse:

Mitglied des Scientific Board of the International Conference of Hyperbolic Problems Theory, Numerics, Applications (Maryland 2008, Beijing 2010, Padua 2012).
Tagungsleitung von mehreren Konferenzen zu den Themen "Hyperbolic Systems", "Discontinuous Galerkin Process" und "Phasetransition" am Mathematischen Forschungsinstitut Oberwolfach.

Betreute Dissertationen und Habilitationen

Dissertationen:

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).

Habilitationen und Postdocs meiner Arbeitsgruppe, die eine Professur erhielten:

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

Publikationen

Zeitschriften | Tagungsbände | Oberwolfach Reports | Bücher | Preprints

Arbeiten in referierten Zeitschriften

1. Kröner, D.: Asymptotic expansions of the pressure and the free boundary for flows through porous media.Manuscr. Math. 44, 131-153 (1983).
2. Kröner, D.; Luckhaus, S.: Flow of oil and water in a porous medium. J. Differ. Equations 55, 276-288 (1984).
3. 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).
4. 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).
5. 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).
6. Kröner, D.: Asymptotic behaviour of the solution of the non-steady dam problem for incompressible fluids.
   Control Cybern. 14, 247-273 (1985).
7. 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).
8. 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).
9. Kröner, 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).
10. 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).
11. Kröner, D.: Absorbing boundary conditions for the linearized Euler equations in 2-D. Math. Comput. 57, No.195, 153-167 (1991).
12. Gilardi, G.; Kröner, D.: The dam problem in unbounded domains. Ann. Mat. Pura Appl., IV. Ser. 164, 321-364 (1993).
13. 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).
14. 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).
15. 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).
16. 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).
17. 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).
18. 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).
19. 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).
20. 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).
21. Klöfkorn, 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).
22. 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.
23. Kröner, D.: Numerics and simulations for convection-dominated problems. Vychisl. Tekhnol. 8, Spec. Iss. 4, 59-71 (2003).
24. 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).
25. 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).
26. 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).
27. Bänsch, E.; Goncharova, O.; Koop, A.; Kröner, D.: Modelling and numerical investigation of fluid structure interaction in the problem with elastic surface. Preprint 2006.
28. 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).
29. 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).
30. 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).
31. Hermsdörfer, K.; Kraus, C.; Kröner, D.: Interface conditions for limits of the Navier-Stokes-Korteweg modell. Submitted to Interfaces and Free Boundaries (2010).
32. 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). (online seit: 18. Januar 2011)
     

Arbeiten in referierten Tagungsbänden

1. 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).
2. 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).
3. 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).
4. 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).   (Inhaltsverzeichnis)
5. 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).
6. 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).   (Inhaltsverzeichnis)
7. 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).
8. 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).
9. 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).
10. 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).   (Inhaltsverzeichnis)
11. 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).
12. 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).   (Inhaltsverzeichnis)
13. 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).
14. 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).   (Inhaltsverzeichnis)
15. 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).   (Inhaltsverzeichnis)
16. 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).   (Inhaltsverzeichnis)
17. 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. (ed.); Krömker, S. (ed.); Rannacher, R. (ed.); Tomi, F. (ed.), Trends in Nonlinear Analysis. Berlin (u.a.) : Springer, 289 - 306 (2003).   (Inhaltsverzeichnis)
18. 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).   (Inhaltsverzeichnis)
19. 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). (Inhaltsverzeichnis)
20. 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). (Inhaltsverzeichnis)
21. 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).
22. 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).
23. 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). (Inhaltsverzeichnis)
24. 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).
25. 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).
26. 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).
27. 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).
28. 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). (Inhaltsverzeichnis)
29. 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).
30. 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).   (Inhaltsverzeichnis)
31. Kröner, D.: Jump conditions across phase boundaries for the Navier-Stokes-Korteweg equation. Submitted to Proceedings of the 13th international conference on hyperbolic problems, June 15-19, 2010, Peking.
32. Kröner, D.; Müller, T.: Related Problems for TV-Estimates for Conservation Laws on Surfaces. Submitted to Proceedings of the 13th international conference on hyperbolic problems, June 15-19, 2010, Peking.
33. 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, Heidelberg : Springer (2012) = Mathematics in Industry 17, Part 6, 561-567 (2012).

Oberwolfach Reports

1. Dafermos, C. M.; Kröner, D.; Leveque, R. J.: Hyperbolic Conservation Laws. In: Abstracts from the Workshop held April 4th– 10th, 2004. Oberwolfach Rep. 1, No. 2, 915–962 (2004).
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. 5, No. 4, 3139-3200 (2008).

Bücher (Autor bzw. Herausgeber)

1. 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.   (Inhaltsverzeichnis)
2. Kröner, D.: Numerical schemes for conservation laws. Wiley-Teubner Series Advances in Numerical Mathematics. Chichester u.a. : Wiley-Teubner 1997.   (Inhaltsverzeichnis - download)
3. 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.   (Inhaltsverzeichnis - download)
4. Herbin, D. (ed.); Kröner, D. (ed.): Finite Volumes for Complex Applications III. Problems and Perspectives. Paris : Hermes Science Publ. 2002. (Inhaltsverzeichnis des Reprints - download)
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.   (Inhaltsverzeichnis)
6. 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.   (Inhaltsverzeichnis)
7. 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.   (Inhaltsverzeichnis)
8. 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.   (Inhaltsverzeichnis)
9. 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.   (Inhaltsverzeichnis)
10. Nagel, W. E.; Kröner, D.; Resch, M. (eds.): High Performance Computing in Science and Energeering '11. Transactions Transactions of the High Performance Computing Center, Stuttgart (HLRS) 2011. Berlin : Springer 2011. (Inhaltsverzeichnis)

Preprints

1. Dziuk, G.; Kröner, D.; Müller, T.: Scalar conservation laws on moving hypersurfaces, Preprint, Freiburg 2012.
2. Chalons, C.; Kröner, D.; Thanh, M. D.: A robust numerical method for approximating solutions of a model of two-phase flows and its properties, Preprint, submitted 2011.

Drittmittelprojekte

Landesstiftung Baden-Württemberg - Förderprogramm "High Performance Computing"

Vorträge, Forschungsaufenthalte, Tagungen

• Sommerschule Bangalore 7/2005
• Forschungsaufenthalt Mittag-Leffler-Institut, Schweden 9/2005
• Hyperbolic Systems Lyon 7/2006
• Sommerschule Cargese 8/2006
• Workshop Heraklion 9/2006
• Workshop Banff, Canada 10/2006
• Vortrag Banja Luka 12/2006
• Forschungsaufenthalt Prag 3/2007
• Vortrag Aachen 5/2007
• Tagung Vancouver 8/2007
• ENUMATH Graz 9/2007
• Tagung Hangzhou, China 10/2007
• Vortrag Karlsruhe 12/2007
• Workshop Straßburg 1/2008
• Miniworkshop Oberwolfach 2/2008
• Tagung Calais 3/2008
• Tagung St. Petersburg 5/2008
• Hyperbolic Systems in Maryland 6/2008
• Heidelberg 7/2008
• Tagung Almati 9/2008
• Tagung Novosibirsk 10/2008
• Berlin 10/2008
• Vortrag Bayreuth 11/2008
• Tagung Oberwolfach 12/2008
• Workshop Aachen 2/2009
• Workshop Stuttgart 2/2009
• Vortrag Stuttgart 2/2009
• DFG-CNRS Workshop Freiburg 3/2009
• DMV 9/2009
• Tagung 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 Tagung Peking 6/2010
• St. Petersburg 9/2010
• Prag 10/2010

Forschungsinteressen

Mehrphasenströmungen mit Phasenübergang: Die mathematische Modellierung von Phasenübergängen in einer Strömung ist ein aktuelles Forschungsgebiet mit vielen offenen Fragen. Insbesondere die thermodynamisch korrekte Formulierung der Phasenübergänge an der Phasengrenze ist eine besondere Herausforderung. Das gleiche gilt für die Entwicklung der zugehörigen numerischen Algorithmen und die numerische Simulation. Als Sprecher einer deutsch-französischen Forschergruppe und durch die Betreuung von Doktoranden sowie durch eigene Untersuchungen arbeite ich auf diesem Gebiet (siehe Drittmittelprojekt DFG Phasefield models).

Numerik für konvektionsdominante partielle Differentialgleichungen: Eine besondere Herausforderung ist nach wie vor die effektive Berechnung von Strömungen, bei denen die Konvektion gegenüber der Viskosität und Diffusion dominant ist. Nur mit Hilfe einer besonderen Stabilisierungstechnik können solche Probleme mit der nötigen Zuverlässigkeit und Effizienz berechnet werden. Für reine Erhaltungsgleichungen in mehreren Raumdimensionen konnten wir die Konvergenz von Finite-Volumen-Verfahren auf unstrukturierten Gittern und a posteriori Fehlerabschätzungen zeigen.

Komplexitätsreduktion: Viele Probleme können erst nach Reduktion ihrer Komplexität effizient berechnet werden. Verschiedene Techniken wie ”reduced basis methods” und ”slow manifolds” führen zu beeindruckenden Erfolgen. Diese Fragen werden in den Arbeiten mit Jung und Haasdonk bzw. in dem Projekt der Baden-Württemberg-Stiftung gemeinsam mit D. Lebiedz bearbeitet (siehe Drittmittelprojekt Landesstiftung Baden-Württemberg).

Vorschläge für Diplomarbeiten und Dissertationen

• 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