Universität Freiburg

German Version

Homepage of Prof. Dr. Dietmar Kröner


Dietmar Kröner
Section of Applied Mathematics
University Freiburg
Hermann-Herder-Str.10

D-79104 Freiburg i. Br.

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

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Main Working Focus | Projects | Current Dissertations | Diploma Thesis to Appoint | Publication List | Released Books | Lecture Examples | Projects | Class Schedules

Main Working Focus

    Numerics for partial differential equations, particularly coonservation equations

    Numerical fluid mechanics

    Free boundary value problems

    Scientific computing

Current Dissertations

 

Diploma Thesis to Appoint

    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

Publication List

1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005


    1983

    Asymptotic Expansions of the Pressure and the Free Boundary for Flow through Porous Media.
    Manuscripta Mathematica 44, 131-153, 1983.

    1984

    I Parabolic Regularization and Behaviour of the Free Boundary for Unsaturated Flow in a Porous Medium.
    Journal für die reine und angewandte Mathematik 348, 180-196, 1984.

    Gemeinsame Arbeit mit S. Luckhaus, Heidelberg.
    Flow of Oil and Water in a Porous Medium .
    Journal of Differential Equations 55, 276 - 288, 1984.

    Die Regularität der Sickerlinie bei einem instationären Grundwasserproblem.
    ZAMM 64, T292-T294, 1984.

    1985

    Ed.: A. Bossavit, A. Damlamian, M. Fremond.
    Global Behaviour of the Solution of the Non-Steady Filtration Problem 2E . Free boundary problems: applications and theory. Vol. III, 1985.

    Gemeinsame Arbeit mit J. F. Rodrigues, Lissabon.
    Global Behaviour for Bounded Solutions of a Porous Media Equation of Elliptic-Parabolic Type 2E.
    Journal de Mathématiques Pures et Appliquées 64, 105-120, 1985.

    Asymptotic Behaviour of the Solution of the Non-Steady Dam Problem fo r Incompressible Fluids. Control and Cybernetics 14, 247-273, 1985.

    1986

    The Regularity of the Free Boundary for a Non-Steady Filtration Problem in the Case of a Compressible Flow.
    Boll. U. M. I. (6), 5. B., 881-906, 1986 2E

    Asymptotische Entwicklungen für Strömungen von Flüssig keiten mit freiem Rand und dynamischem Kontaktwinkel.
    (Habilitationschrift) Preprint 809, SFB 72, Bonn, 1986.

    1987

    The Flow of a Fluid with a Free Boundary and Dynamic Contact Angle.
    ZAMM 67 5, T304-T306, 1987.

    Ed.: P. Concus, R. Finn.
    Large Time Behaviour for the Solution of the Non-Steady Dam Problem.
    Variational methods for free surface interfaces, Springer, 1987.

    Directionally Adapted Upwind Schemes for the Euler Equations in 2-D.
    Notes on Numerical Fluid Mechanics, Finite Approximations in Fluid Mechanics II , DFG-Priority Research Program, Results 1986-1988, Vieweg Verlag.

    1988

    Ed.: Masuda, Rautmann, Solonikov.
    A Flow with a Free Boundary and Dynamic Contact Angle.
    Konferenzbericht über die Navier-Stokes-Tagung in Oberwolfach, 1988.

    1989

    Ed.: Ballmann, Jeltsch
    Numerical Schemes for the Euler Equations in Two Space Dimensions without Dimensional Splitting. Nonlinear Hyperbolic Equations-Theory, Computational Methods and Applications. Notes on Numerical Fluid Mechanics, 1989.

    Gemeinsame Arbeit mit Prof. Kenmochi und Dr. Kubo, Chiba (Japan).
    Periodic Solutions to Porous Media Equations of Parabolic-Elliptic Type.
    Preprint 1989, Journal of Partial Differential Equations.

    About Splitting and Non-Splitting Schemes for the Euler Equations in 2-D.
    Proceedings of the Eighth GAMM Conference on Numerical Methods in Fluid Mechanics, Ed.: Wesseling, Delft, 1989.

    Gemeinsame Herausgabe mit Prof. Bemelmans.
    Workshop ''Navier-Stokes equations''.
    Saarbrücken 1989. Abstracts, Schriftenreihe des Institutes für Mathematik der Universität des Saarlandes, 1989.

    1990

    Gemeinsame Arbeit mit Professor Gilardi, Pavia.
    The Dam Problem for Unbounded Domains.
    Preprint 1990, Comm. PDE.

    1991

    Absorbing Boundary Conditions for the Linearized Euler Equations in 2D. Mathematics of Computation, Vol. 57, No. 195, 153-167, 1991.

    1992

    Finite volume methods for conservation laws.
    Proceedings of the Int. Conf. on Computations of Differential Equations and Dynamical Systems. Eds.: Kang Feng, Zhong-Ci Shu, 1992, 11-25.

    Gemeinsame Arbeit mit M. Rokyta, Prag.
    Convergence of Upwind Finite Volume Schemes for Scalar Conservation Laws in 2D.
    Preprint 1992, SFB256, Bonn, SIAM J. Num. Anal. 1994 (4).

    Gemeinsame Arbeit mit Dr. Noelle (Universität Bonn) und Dr. Rokyta (Prag).
    Convergence of Higher Order Finite Volume Schemes on Unstructured Grids for Scalar Conservation Laws in Two Space Dimensions.
    Preprint 1992, SFB2 56, Bonn, Numer. Math. 1995.

    Gemeinsame Arbeit mit M.Geiben, S.Noelle (beide Universität Bonn) und M.Rokyta (Prag).
    A Lax-Wendroff Type Theorem for Cell-Centered Finite Volume Schemes in 2D.
    Preprint 1991. SFB256, Bonn, Germany.

    1993

    Gemeinsame Arbeit mit B. Beinert
    Finite volume methods with local mesh alignment.
    Proceedings of the 10th-GAMM Seminar, Kiel 1993, Notes on Numerical Fluid Mechanics, Vieweg 1994.

    1995

    In Eds.: Galdi,G.P., Malek, J., Necas, J.
    Finite volume methods in fluid mechanics. Progress in theoretical and computational fluid mechanics.
    Pitman Research Notes in Mathematical Series, 1994.

    1995

    Gemeinsame Arbeit mit Zajaczkowski.
    Measure-valued solutions of the Euler equations for ideal compressible polytropic fluids.
    Mathematical Methods in the Applied Sciences, 1995.

    Gemeinsame Arbeit mit A. Koop , S. Müller, B. Schupp, S. Schmitz, B. Schroeter.
    Deformation einer elastischen Flexlippe.
    Erscheint im Tagungsband über das Statusseminar des Verbundforschungsprojektes Mathematik des BMBF, München 1995.

    Gemeinsame Arbeit mit M. Rokyta, M. Wierse.
    Error estimates for higher order flux-limiter schemes for convection dominated diffusion problems in 2-D. Manuskript.

    Gemeinsame Arbeit mit W. Zajaczkowski.
    Flows with free boundary and dynamic contact angle in 3-D, I.
    Manuskript.

    Gemeinsame Arbeit mit W. Zajaczkowski.
    Flows with free boundary and dynamic contact angle in 3-D, II.
    Manuskript.

    1996

    Numerical studies for flows with free boundary and dynamic cantact angle.
    Preprint Nr. 26 / 1999, Albert-Ludwigs-Universität Freiburg, Mathematische Fakultät. Eingereicht bei ZAMM.

    Ed.: W. Borchers, G. Domick, D. Kröner, R. Rautmann, D.Sauper
    Visualization methods in high performance computing and flow simulation.
    VSP Utrecht 1996

    Gemeinsame Arbeit mit M. Wierse, T. Geßner.
    Numerical methods, simulations and visualization for compressible flow problems.
    Proceedings Visualization and Mathematics (Eds.: H.-Ch. Hege, K. Polthier) Springer 1996, Heidelberg.

    Gemeinsame Arbeit mit T. Geßner, B. Schupp, M. Wierse.
    Finite volume methods for conservation laws and convection dominated diffusion equations. Proceedings of the conference: Finite volume schemes 1996.

    Gemeinsame Arbeit mit M. Rokyta, M. Wierse.
    Finite volume methods of higher order for conservation laws and convection dominated diffusion equations.
    Proceedings of the conference: 2nd Seminar Euler and Navier-Stokes Equations, Praque 1996.

    < P> Gemeinsame Arbeit mit M. Rokyta.
    A Lax-Wendroff type theorem for upwind finite volume schemes in 2-D. East-West J. Numer. Math., Vol. No.4, pp. 279-292, 1996.

    Gemeinsame Arbeit mit M. Wierse.
    Higher order upwind schemes on unstructured grids for the nonstationary compressible Navier-Stokes equations in complex timedependent geometries in 3D.
    Preprint 1996, 2, Universität Freiburg.

    Gemeinsame Arbeit mit T. Geßner, B. Schupp, M. Wierse.
    Finite volume methods for conservation laws and convection dominated diffusion equations.
    Preprint 1996, 28, Universität Freiburg.

    Gemeinsame Arbeit mit M. Rokyta.
    A priori error estimates for upwind finite volume schemes in several space dimensions.
    Preprint 1996, 37, Universität Freiburg.

    Gemeinsame Arbeit mit M. Wierse, A. Müller, B. Schupp, R. Schwörer.
    Simulation of a 3-D piston driven flow.
    Proceedings of the 5th CNRS-DFG workshop on Numericalflow simulation, München, Germany, December 6-7, 1996. Vieweg: Notes on Numerical Fluid Mechanics 64.

    1997

    Gemeinsame Arbeit mit M. Rokyta
    Higher Order finite volume methods for convection dominated diffussion equation in 2D.
    In: Numerical Modelling in Continuum Mechanics Feistauer M., Rannacher R. , Kozel K. (eds.), 62-70, Matfyzpress, Praha, (1997).

    Kröner, D; Koop, A; Schupp, B; Müller, S; Schmitz, S; Schoeter, B.
    Deformation einer elastischen Flexlippe.(Deformation of an elastic cylindrical tube).(German)
    Hoffmann, Karl-Heinz (ed.) et al., Mathematik: Schlüsseltechnologie für die Zukunft.Verbindungsprojekte zwischen UniversitäT und Industrie.
    Berlin: Springer. 177-189 (1997)

     

    1998
    Finite volume schemes in multidimensions.
    d.F. Griffiths, D.J. Highman (eds), G.A. Watson, Pitman research Notes in Mathematics Series 380, Numerical analysis 1997, 179-192 (1998)

    Gemeinsame Arbeit mit A. Egelja, R. Schwörer, N.Lanson, M. Mancip, J.P. Vila
    Combined Finite Volume and Smoothed Particle Method.
    In: Numerical Flow Simulation I; CNRS-DFG Collaborative Research Programme, Results 1996-1998, E.H. Hirschel (ed), Vieweg 1998.

    1999

    Combined finite volume and smoothed particle method.
    Notes on Numerical Fluid Mechanics, Vol. 52, Numerical Flow Simulation I 1999

    Gemeinsame Arbeit mit M. Rokyta.
    Higher order error estimates for time-dependent convection dominated diffusion equations in 2-D.
    Manuskript.

    Gemeinsam mit M.Ohlberger und C.Rohde (Eds.)
    An Introduction to recent development in theory and numerics for conservation laws.
    Lecture Notes in Computational Science and Engineering, Springer 1999.

     

    2000

    Gemeinsame Arbeit mit M. Ohlberger
    A posteriori error estimates for upwind finite volume schemes in several space dimensions.
    Math. Comput. 69 (2000), 25-39.

    Gemeinsame Arbeit mit L.Klassen A.Klimmek, D.Trescher
    Numerical optimization of scavenging in two-stroke engines with transfer ducts, an exhaust port and a moving piston.
    Erscheint in: Mathematik - Schlüsseltechnologie für die Zukunft, Tagungsband des BMBF-Statusseminars der anwendungsorientierten Verbundprojekte Verbundprojekte auf dem Gebiet der Mathematik, 2000.

    Gemeinsame Arbeit mit W. Zajaczkowski.
    Flows with free boundary and dynamic contact angle in 3-D, I.
    Manuskript.

    Gemeinsame Arbeit mit W. Zajaczkowski.
    Flows with free boundary and dynamic contact angle in 3-D, II.
    Manuskript.

     

    2001

    Gemeinsame Arbeit mit A.Dedner, I.L. Sofronov, und M. Wesenberg.
    Transparent Boundary Conditions for MHD Simulations in Stratified Atmospheres.
    Preprint Nr. 26 / 2000, Albert-Ludwis-Universität Freiburg, Mathematische Fakultät; Journal of Computational Physics 171, 448-478 (2001).

    Gemeinsame Arbeit mit B. Haasdonk und C. Rohde.
    Convergence of a Staggered-Lax-Friedrichs-Scheme on Unstructured Grids in 2D. Numer. Math. 88, 459-484 (2001).

    Gemeinsame Arbeit mit A. Dedner, C. Rohde and M. Wesenberg.
    Godunov-type schemes for the MHD equations, Godunov Methods: Theory and Applications.
    (E.F. Toro, ed.), Kluwer Academic/Plenum Publishers, 2001, p. 209-216.

    Gemeinsame Arbeit mit A. Dedner, I.L. Sofronov und M. Wesenberg.
    Absorbing Boundary Conditions for Astrophysical MHD Simulations.
    In: Godunov Methods: Theory and Applications 2001, New York, p. 217-224. Ed.: E.F. Toro (2001).

    Gemeinsame Arbeit mit T. Gessner.
    Godunov Type Methods on Unstructured Grids and Local Mesh Refinement.
    In: Godunov Methods: Theory and Applications,New York, 527-548. Ed.: E.F. Toro (2001).

    Gemeinsame Arbeit mit M. Ohlberger and C. Rohde.
    A posteriori error estimates and adaptives methods for hyperbolic and convection dominated parabolic conservation laws.
    submitted to Proc. Trend in Nonlinear Analysis, Heidelberg 2001.

    Gemeinsame Arbeit mit T. Geßner
    Dynamic Mesh Adaption for Supersonic Reactive Flow.
    Proceedings of the Eighth International Conference on Hyperbolic Problems: Theory, Numerics, Application. Magdeburg, 2001, p. 415-424.

    Gemeinsame Arbeit mit A. Dedner und M. Wesenberg
    MHD instabilities arising in solar physics: a numerial aproach.
    Proceedings of the Eighth International Conference on Hyperbolic Problems: Theory, Numerics, Applications. Magdeburg, 2001, p. 277-286.

     

    2002

    Gemeinsame Arbeit mit R. Klöfkorn, M. Ohlberger.
    Local adaptive methods for convection dominated problems.
    Erscheint in International Journal for Numerical Methods in Fluids 2002.

    Gemeinsame Arbeit mit A. Dedner, F. Kemm, C.-D. Munz, T.Schnitzer und M.Wesenberg.
    Hyperbolic Divergence Cleaning for MHD Equations.
    Journal of Computational Physics, Vol. 175, p. 645-673, (2002) .

    Gemeinsame Arbeit mit L. Klassen und Ph. Schott
    Finite volume method on unstructured grid in 3D with applications to the simulation of gravitiy waves.
    Erscheint in Meterology and Atmospheric Physics.

    Gemeinsame Arbeit mit O. Gontscharowa, W. Dörfler.
    Numerical studies for flows with free boundary and dynamic contact angle.
    ZAMM82 (2002), 167-176.

    Herbin, Raphaele (ed.); Kröner, Dietmar (ed.)
    Finite volumes for complex applications III. Problems and perspectives.
    Papers from the 3rd symposium of finite volumes for complex applications, Porquerolles, France, June 24 - 28, 2002

     

    2003

    Dedner, A.; Kröner, D; Rohde, C.; Snitzer, T.; Wesenberg, M.
    Comparision of finite volume and discontinuous Galerkin methods of higher order for systems of conservation laws in multiple space dimensions. (Englisch)
    Hildebrandt, Stefan (ed.) et al., Geometric analusis and nonlinear partial differential equations.
    Berlin: Springer. 573-589 (2003) .

    Dedner, A; Kröner, D;Rohde, C;Wesenberg, M.
    Efficient divergence cleaning in three-dimensional MHD simulations. (Englisch)
    Krause, Egon (ed.) et al., High perfomance computing in science and engineering '02. Transactions of the High Perfomance Computing Center Stuttgart (HLRS) 2002. Proceedings of the 5th results and review workshop, Stuttgart, Germany, September 30-October 1, 2002 .
    Berlin: Springer. 323-334 (2003).

    Gemeinsam mit L. Klassen, A. Klimmeck, D. Trescher
    Numerical optimisation of scavenging in two-stroke engines with transfer ducts, an exhaust port and moving piston.
    In: W. Jäger: Mathematics. Key Technology for the Future.

    Gemeinsam mit M. Küther, M. Ohlberger, C. Rohde
    A posteriori error estimates and adaptive methods for hyperbolic and convection dominated parabolic conservation laws.
    In: M. Kirkilionis et al., Trends in nonlinear Analysis, Springer, Berlin, 2003

    Kröner, Dietmar
    Numerics and simulations for convection-dominated problems.
    Vychisl. Tekhnol. 8, Spec. Iss. 5, 59 - 71 (2003)

    2004

    Dietmar Kröner and Mai Duc Thanh
    On the Model of Compressible Flows in a Nozzle: Mathematical Analysis and Nu- merical Methods.
    Proceedings of the International Conference on hyperbolic problems, 2004

    2005

    Nicolas Besse and Dietmar Kröner.
    Convergence of locally divergence-free discontinuous-Galerkin methods for the induction equations of the 2D-MHD system.
    M2AN, 2005

    O.A. Kovyrkina, D. Kröner, V.V. Ostapenko
    On monotone reconstruction of difference solution at isolated discontinuity.
    Preprint 2005

    Dietmar Kroener, Philippe G. Lefloch and Mai Duc Thanh
    Nozzle Problem: Stability, Entropie and Numerics.
    Preprint 2005

    Martin Nolte, Dietmar Kröner.
    Well-Balanced Schemes for the Initial Boundary Value Problem for 1D Scalar Conservation Laws.
    Preprint 2005

    Dietmar Kröner and Mai Duc Thanh.
    On fluid flows in a moving discontinuous nozzle: modeling, riemann solutions and numerics.
    SIAM Journal on Numerical Analusis, 2005

Released Books

    Visualization. Proceedings of the International Workshop on Visualiza tion.
    Paderborn 1995.

    Numerical Schemes for Conservation Laws.
    Wiley und Teubner, 480 Seite n, 1996

    D.Kröner, M.Ohlberger, C.Rhode (Eds.).
    An Introduction to Recent Developments in Theory and Numerics for Conservation Laws.
    Lecture Notes in Computional Science and Engineering, Vol.5, 1998.

    Gemeinsam mit R. Herbin
    Finite volumes for complex applications III. Problems and Perspectives.
    Hermes, Paris, 2002.

Projects

DFG-Schwerpunktprogramm: MHD-Gleichungen und Strahlungstransport

DFG-Projekt: Entwicklung und Implementierung eines Finite-Element-Verfahren zur Berechnung der Deformation elastischer Strukturen durch inkompressible Strömungen

BMBF-Förderschwerpunkt Neue Mathematische Verfahren in Industrie und Dienstleistungen : Detaillierte Simulation des Ladungswechsels in Zweitaktmotoren

BMBF-Projekt: Transportmodellierung

BMBF-Project: Brennstoffzelle

DFG-Project: Minimal orbits and Hamilton Jacobi.

DFG-Project: Phase transitions in thermoelasticity and compressible fluids.

DFG-Forschergruppe: "Nonlinear Partial Differential Equations: Theoretical and Numerical Analysis"

DGF-Project: "Micro-Macro Modelling and Simulation of Liquid-Vapor Flows"

BMBF-Project: "Dreidimensionale Simulation von Brennstoffzellen"

Landesstiftung Baden-Württemberg: "3D-Simulation magnetohydrodynamischer Instabilitäten in Akkretionsscheiben"