Prof. Dr. Jan Giesselmann

Contact

work +49 6151 16-23167

Work S4|10 108
Dolivostraße 15
64293 Darmstadt

Research Interests

  • Hyperbolic Conservation Laws
  • Compressible fluid flows
  • Discontinuous Galerkin Methods
  • A-priori and a-posteriori error estimators
  • Model-adaptation
  • Uncertainty Quantification

Teaching

Summer Term 2021

  • Numerical Linear Algebra
  • Numerical Mathematics (Math 4 for mech. engineering)
  • BSc Seminar Numerics

This is a list of suggestions for Bsc-Thesis topics that I would be happy to supervise. If you are interested in any of these topics please send me a mail. The topic will be made precise once we have discussed your scientific background and interests,

I give links to the literature for each topic. The literature is supposed to convey an impression of what the topic is about. It is not necessary to understand this literature in detail before working on any of the topics.

BSc

MSc



Winter Term 2020/21
  • Lecture Numerics of Ordinary Differential Equations (German)
  • Mathematical Consulting: Introduction to Mechanical Engineering
  • Proseminar : Numerical Mathematics


Sommersemester 2020


Winter Term 2019/20
Summer Term 2019Wintersemester 2018/19
Sommersemester 2018
Uncertainty Quantification (RWTH Aachen)
Mathematische Grundlagen für Computational Engineering Science II (RWTH Aachen)
Wintersemester 2017/18
Mathematische Grundlagen für Computational Engineering Science I (RWTH Aachen)
Mathematische Grundlagen für Computational Engineering Science V (RWTH Aachen)
Sommersemester 2017
Numerical Methods for Differential Equations (Uni Stuttgart)
Masterseminar Mehrskalenmodellierung (Uni Stuttgart)
Wintersemester 2016/17
Einführung in die Numerik Partieller Differentialgleichungen (Uni Stuttgart)
Sommersemester 2016
Numerical Methods for Differential Equations (Uni Stuttgart)
Wintersemester 2015/16
Einführung in die Numerik Partieller Differentialgleichungen (Uni Stuttgart)
Sommersemester 2015
Numerical Methods for Differential Equations (Uni Stuttgart)
Masterseminar Diskontinuitäten im Kontinuum (Uni Stuttgart)
Proseminar Iterative Lösungsverfahren (Uni Stuttgart)
Wintersemester 2014/15
Lineare Strukturen (Uni Stuttgart)
Sommersemester 2014
Numerische Methoden des Strömungsmechanik (Uni Stuttgart)
Wintersemester 2013/14
Einführung in die Numerik Partieller Differentialgleichungen (Uni Stuttgart)
Proseminar Mathematische Modellierung (Uni Stuttgart)
Sommersemester 2013
Numerische Lineare Algebra (Uni Stuttgart)
Sommersemester 2012
Numerical Methods for Differential Equations (Uni Stuttgart)

Giesselmann, Jan ; LeFloch, Philippe G. (2020):
Formulation and convergence of the finite volume method for conservation laws on spacetimes with boundary.
In: Numerische Mathematik, 144, pp. 751-785. Springer, ISSN 0029-599X,
DOI: 10.1007/s00211-020-01101-7,
[Article]

Giesselmann, Jan ; Meyer, Fabian ; Rohde, Christian (2020):
A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws.
In: BIT Numerical Mathematics, [Article]

Sarna, Neeraj ; Giesselmann, Jan ; Torrilhon, Manuel (2020):
Convergence Analysis of Grad's Hermite Expansion for Linear Kinetic Equations.
In: Siam Journal on Numerical Analysis, 58 (2), pp. 1164-1194. ISSN 0036-1429,
DOI: 10.1137/19M1270884,
[Article]

Dedner, Andreas ; Giesselmann, Jan ; Pryer, Tristan ; Ryan, Jennifer K (2019):
Residual estimates for post-processors in elliptic problems.
ArXiv, [Other]

Giesselmann, Jan ; Meyer, Fabian ; Rohde, Christian (2019):
Error control for statistical solutions.
[Other]

Meyer, Fabian ; Rohde, Christian ; Giesselmann, Jan (2019):
A posteriori error analysis for random scalar conservation laws using the stochastic Galerkin method.
In: IMA Journal of Numerical Analysis, ISSN 0272-4979,
DOI: 10.1093/imanum/drz004,
[Article]

Dedner, Andreas ; Giesselmann, Jan (2018):
Residual error indicators for discontinuous Galerkin schemes for discontinuous solutions to systems of conservation laws.
In: Springer Proc. Math. Stat., 236, In: Theory, numerics and applications of hyperbolic problems. I, pp. 459-471, Springer, [Book Section]

Giesselmann, Jan ; Kolbe, Niklas ; Lukacova-Medvidova, Maria ; Sfakianakis, Nikolaos (2018):
Existence and uniqueness of global classical solutions to a two species cancer invasion haptotaxis model.
In: Discrete & Continuous Dynamical Systems - B, 23 (10), pp. 4397-4431. [Article]

Giesselmann, Jan ; Zacharenakis, Dimitrios (2018):
A posteriori analysis for the Euler-Korteweg model.
In: Springer Proc. Math. Stat., 236, In: Theory, numerics and applications of hyperbolic problems. I, pp. 631-642, Springer, [Book Section]

Giesselmann, Jan ; Lattanzio, Corrado ; Tzavaras, Athanasios E. (2017):
Relative energy for the Korteweg theory and related Hamiltonian flows in gas dynamics.
In: Arch. Ration. Mech. Anal., 223, pp. 1427 - 1484. DOI: 10.1007/s00205-016-1063-2,
[Article]

Giesselmann, Jan ; Pryer, Tristan
Cances, Clement ; Omnes, Pascal (eds.) (2017):
Goal-oriented error analysis of a DG scheme for a second gradient elastodynamics model.
In: Springer Proceedings in Mathematics & Statistics, 199, Finite Volumes for Complex Applications VIII-Methods and Theoretical Aspects, [Conference or Workshop Item]

Giesselmann, Jan ; Pryer, Tristan (2017):
A posteriori analysis for dynamic model adaptation in convection dominated problems.
In: Math. Models Methods Appl. Sci. (M3AS), 27 (13), pp. 2381 - 2423. DOI: 10.1142/S0218202517500476,
[Article]

Giesselmann, Jan ; Tzavaras, Athanasios E. (2017):
Stability properties of the Euler-Korteweg system with nonmonotone pressures.
In: Appl. Anal., 96 (9), pp. 1528 - 1546. DOI: 10.1080/00036811.2016.1276175,
[Article]

Dedner, Andreas ; Giesselmann, Jan (2016):
A posteriori analysis of fully discrete method of lines DG schemes for systems of conservation laws.
In: SIAM J. Numer. Anal., 54 (6), pp. 3523-3549. [Article]

Giesselmann, Jan (2016):
Relative entropy based error estimates for discontinuous Galerkin schemes.
In: Bull. Braz. Math. Soc. (N.S.), 47 (1), pp. 359-372. ISSN 1678-7714,
DOI: 10.1007/s00574-016-0144-z,
[Article]

Giesselmann, Jan ; LeFloch, Philippe G. (2016):
Formulation and convergence of the finite volume method for conservation laws on spacetimes with boundary.
[Book]

Giesselmann, Jan ; Pryer, Tristan (2016):
Reduced relative entropy techniques for a posteriori analysis of multiphase problems in elastodynamics.
In: IMA J. Numer. Anal., 36 (4), pp. 1685 - 1714. [Article]

Giesselmann, Jan ; Pryer, Tristan (2016):
Reduced relative entropy techniques for a priori analysis of multiphase problems in elastodynamics.
In: BIT Numerical Mathematics, 56, pp. 99 - 127. DOI: 10.1007/s10543-015-0560-2,
[Article]

Giesselmann, Jan (2015):
Low Mach asymptotic preserving scheme for the Euler-Korteweg model.
In: IMA J. Numer. Anal., 32 (2), pp. 802-832. DOI: 10.1093/imanum/dru022,
[Article]

Giesselmann, Jan (2015):
Relative entropy in multi-phase models of 1d elastodynamics: Convergence of a non-local to a local model.
In: J. Differential Equations, 258, pp. 3589-3606. [Article]

Giesselmann, Jan ; Makridakis, Charalambos ; Pryer, Tristan (2015):
A posteriori analysis of discontinuous Galerkin schemes for systems of hyperbolic conservation laws.
In: SIAM J. Numer. Anal., 53, pp. 1280-1303. [Article]

Giesselmann, Jan ; Pryer, Tristan (2015):
Energy consistent discontinuous Galerkin methods for a quasi-incompressible diffuse two phase flow model.
In: M2AN Math. Model. Numer. Anal., 49 (1), pp. 275-301. [Article]

Aki, G.~L. ; Dreyer, W. ; Giesselmann, J. ; Kraus, C. (2014):
A quasi-incompressible diffuse interface model with phase transition.
In: Math. Models Methods Appl. Sci., 24 (5), pp. 827-861. DOI: 10.1142/S0218202513500693,
[Article]

Dreyer, Wolfgang ; Giesselmann, Jan ; Kraus, Christiane (2014):
Modeling of compressible electrolytes with phase transition.
[Book]

Dreyer, Wolfgang ; Giesselmann, Jan ; Kraus, Christiane (2014):
A compressible mixture model with phase transition.
In: Physica D, 273/274, pp. 1-13. DOI: 10.1016/j.physd.2014.01.006,
[Article]

Giesselmann, Jan (2014):
A Relative Entropy Approach to Convergence of a Low Order Approximation to a Nonlinear Elasticity Model with Viscosity and Capillarity.
In: SIAM J. Math. Anal., 46 (5), pp. 3518-3539. DOI: 10.1137/140951710,
[Article]

Giesselmann, Jan ; Makridakis, Charalambos ; Pryer, Tristan (2014):
Energy consistent DG methods for the Navier-Stokes-Korteweg system.
In: Math. Comp., 83, pp. 2071 - 2099. DOI: 10.1090/S0025-5718-2014-02792-0,
[Article]

Giesselmann, Jan ; Müller, Thomas
Fuhrmann, J. ; Ohlberger, M. ; Rohde, C. (eds.) (2014):
Estimating the Geometric Error of Finite Volume Schemes for Conservation Laws on Surfaces for generic numerical flux functions.
In: Springer Proceedings in Mathematics & Statistics, 77, In: Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects, pp. 323-332, Cham, Springer, [Book Section]

Giesselmann, Jan ; Müller, Thomas (2014):
Geometric error of finite volume schemes for conservation laws on evolving surfaces.
In: Numer. Math., 128 (3), pp. 489�516. Springer Berlin Heidelberg, ISSN 0029-599X,
DOI: 10.1007/s00211-014-0621-5,
[Article]

Giesselmann, Jan ; Pryer, Tristan
Fuhrmann, J. ; Ohlberger, M. ; Rohde, C. (eds.) (2014):
On aposteriori error analysis of DG schemes approximating hyperbolic conservation laws.
In: Springer Proceedings in Mathematics & Statistics, 77, In: Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects, pp. 313-322, Cham, Springer, [Book Section]

Giesselmann, Jan ; Tzavaras, Athanasios E.
Ancona, F. ; Bressan, A. ; Marcati, P. (eds.) (2014):
On cavitation in elastodynamics.
pp. 599-606, AIMS, Hyperbolic Problems: Theory, Numerics, Applications, [Conference or Workshop Item]

Giesselmann, Jan ; Tzavaras, Athanasios E. (2014):
Singular Limiting Induced from Continuum Solutions and the Problem of Dynamic Cavitation.
In: Arch. Ration. Mech. Anal., 212 (1), pp. 241 - 281. ISSN 0003-9527,
DOI: 10.1007/s00205-013-0677-x,
[Article]

Giesselmann, Jan (2013):
Cavitation and Singular Solutions in Nonlinear Elastodynamics.
pp. 363-364, Wiley, PAMM 13, DOI: 10.1002/pamm.201310177,
[Conference or Workshop Item]

Giesselmann, Jan ; Miroshnikov, Alexey ; Tzavaras, Athanasios E. (2013):
The problem of dynamic cavitation in nonlinear elasticity.
Séminaire Laurent Schwartz � EDP et applications, [Conference or Workshop Item]

Aki, Gonca L. ; Daube, Johannes ; Dreyer, Wolfgang ; Giesselmann, Jan ; Kränkel, Mirko ; Kraus, Christiane (2012):
A diffuse interface model for quasi-incompressible flows : Sharp interface limits and numerics.
pp. 54-77, ESAIM Proceedings Vol. 38, DOI: 10.1051/proc/201238004,
[Conference or Workshop Item]

Audusse, Emmanuel ; Berthon, Christiophe ; Chalons, Christophe ; Delestre, Olivier ; Goutal, Nicole ; Jodeau, Magali ; Sainte-Marie, Jaques ; Giesselmann, Jan ; Sadaka, Georges (2012):
Sediment transport modelling : Relaxation schemes for Saint-Venant - Exner and three layer models.
pp. 78-98, ESAIM Proceedings Vol. 38, DOI: 10.1051/proc/201238005,
[Conference or Workshop Item]

Dreyer, Wolfgang ; Giesselmann, Jan ; Kraus, Christiane ; Rohde, Christian (2012):
Asymptotic Analysis for Korteweg Models.
In: Interfaces Free Bound., 14, pp. 105 - 143. [Article]

Giesselmann, Jan
Li, T. ; Jiang, S. (eds.) (2012):
Sharp interface limits for Korteweg Models.
2, pp. 422 - 430, Hyperbolic Problems: Theory, Numerics, Applications, [Conference or Workshop Item]

Giesselmann, Jan ; Wiebe, Maria
E. Vasquez-Cendon A. Hidalgo, P. Garcia Navarro (ed.) (2012):
Finite volume schemes for balance laws on time-dependent surfaces.
Taylor and Francis Group, Numerical Methods for Hyperbolic Equations, [Conference or Workshop Item]

Giesselmann, Jan (2011):
Modelling and Analysis for Curvature Driven Partial Differential Equations.
Universität Stuttgart,
[Ph.D. Thesis]

Giesselmann, Jan (2009):
A convergence result for finite volume schemes on Riemannian manifolds.
In: M2AN Math. Model. Numer. Anal., 43 (5), pp. 929-955. [Article]

Giesselmann, Jan
Eymard, R. ; Herard, J.-M. (eds.) (2008):
Convergence Rate of Finite Volume Schemes for Hyperbolic Conservation Laws on Riemannian Manifolds.
ISTE, Wiley, Finite Volumes for Complex Applications 5, [Conference or Workshop Item]

Education
2001 Abitur, Widukind Gymnasium Enger
2006 Diplom in Mathematics, University of Bielefeld
2011 PhD in Mathematics, University of Stuttgart
2015 Habilitation in Mathematics, University of Stuttgart
Academic Career
2007 – 2018 Research and Teaching Assistant University of Stuttgart
2011/12 Postdoc, University of Crete
2012/13 Research Assistant, Weierstrass Institute, Berlin
2013/14 Associate Professor (not tenured) “Numerical Mathematics” University of Stuttgart
2015 – 17 Associate Professor (not tenured) “Optimisation and Inverse Problems” University of Stuttgart
2017/18 Associate Professor (not tenured) “Numerical Simulations” RWTH Aachen University
since October 2018 Professor “Numerics” Technische Universität Darmstadt

Observer-based data assimilation for time-dependent flows in gas networks (Subproject C05 in SFB-TRR154 funded by German Research Foundation DFG) This is a joint project with Martin Gugat, FAU Erlangen-Nuremberg

Tristan Pryer (Univ. of Bath) and I were organising a minisymposium on “Numerical methods for Hyperbolic Conservation Laws” at Computational Methods in Applied Mathematics that has been postponed to 2021 due to COVID 19.

Some conference videos:

Dynamical, spatially heterogeneous model adaptation in compressible flows (funded by German research foundation (DFG))

Numerical methods for multi-phase flows with strongly varying Mach numbers Elite-program for Postdocs of Baden-Wuerttemberg Stiftung

Mathematical Modeling of compressible fluids – from wild solutions to data integration – Research Seed Capital of University of Stuttgart and Ministry of Science, Research and Art Baden-Württemberg