Prof. Dr. Jens Lang

Numerics of partial differential equations

Contact

work +49 6151 16-23160
fax +49 6151 16-23164

Work S4|10 102
Dolivostraße 15
64293 Darmstadt

Research

  • Adaptivity, (stochastic) FEM and FVM, moving and anisotropic meshes
  • A posteriori error estimation and global error control
  • Linearly implicit time integrators for stiff problems
  • Adaptive large eddy simulation in reactive flows
  • ODE and PDE constrained optimal control
  • Modelling, simulation and optimization of water/gas networks
  • Uncertainty quantification with random PDEs
  • Model order reduction and machine learning

News

IACM, 5th International Conference on Computational Methods for Multi-scale, Multi-uncertainty and Multi-physics Problems, Porto, Portugal, 1-4 July 2025
AFRICOMP7, 7th African Conference on Computational Mechanics, Cape Town, South Africa, 25-27 February 2026
FoCM2026, Conference on Foundations of Computational Mathematics, Wien, Austria, 8-18 July 2026
WCCM2026, 17th World Congress on Computational Mechanics, Munich, Germany, 19-24 July 2026

Editorial Boards

Editor of the Journal Applied Numerical Mathematics, 2006-2022

›Publications

Technische Universität Darmstadt
WS 2025/26 Numerics for PDEs with Uncertain Data
Bachelor Seminar on Numerics
SS 2025 on sabbatical
WS 2024/25 Numerics of ODEs
Proseminar
SS 2024 Introduction to Mathematical Modelling
Numerical Linear Algebra
Proseminar
WS 2023/24 Introduction to Numerics
Master Seminar on Numerics
Proseminars
SS 2023 Introduction to Mathematical Modelling
Numerics of Hyperbolic Equations
Stochastic Finite Elements
Master Seminar on Numerics
WS 2022/23 Numerics of PDEs
Bachelor Seminar on Numerics
SS 2022 Introduction to Mathematical Modelling
Numerical Linear Algebra
Bachelor Seminar on Numerics
WS 2021/22 Numerics of ODEs
Numerics of Hyperbolic Equations
SS 2021 on sabbatical
WS 2020/21 Introduction to Numerics
Master Seminar on Numerics
SS 2020 Numerics of Hyperbolic Equations
Stochastic Finite Elements
Master Seminar on Numerics
WS 2019/20 Numerics of PDEs
Bachelor Seminar on Numerics
SS 2019 Introduction to Mathematical Modelling
Stochastic Finite Elements
Bachelor Seminar on Numerics
WS 2018/19 Numerics of ODEs
Bachelor Seminar on Numerics
SS 2018 Numerical Linear Algebra
Numerics of Hyperbolic Equations
Bachelor Seminar on Numerics
WS 2017/18 Introduction to Numerics
Bachelor/Master Seminar on Numerics
SS 2017 on sabbatical
WS 2016/17 Theory of ODEs/PDEs for Mechanical Engineers
Numerics of Hyperbolic Equations
Bachelor/Master Seminar on Numerics
SS 2016 Introduction to Mathematical Modelling
Master Seminar on Numerics
WS 2015/16 Numerics of PDEs
SS 2015 Numerics of Hyperbolic Equations
Bachelor/Master Seminar on Numerics
WS 2014/15 Introduction to Numerics
Bachelor/Master Seminar on Numerics
SS 2014 Numerics for Mechanical Engineers
Bachelor/Master Seminar on Numerics
WS 2013/14 Numerics of Evolutionary Equations
Bachelor/Master Seminar on Numerics
Proseminar Introduction to Mathematical Modelling
SS 2013 on sabbatical
WS 2012/13 Theory of ODEs/PDEs for Mechanical Engineers
Numerics of ODEs
Bachelor/Master Seminar on Numerics
SS 2012 Numerics of Hyperbolic Equations
Numerics of Large Stiff ODEs
Bachelor/Master Seminar on Numerics
WS 2011/12 Introduction to Numerics
Numerics of Parabolic Equations
Bachelor/Master Seminar on Numerics
SS 2011 Numerics for Mechanical Engineers
Numerics of Elliptic Equations
Bachelor/Master Seminar on Numerics
WS 2010/11 Theory of ODEs/PDEs for Mechanical Engineers
Numerics of ODEs
Bachelor/Master Seminar on Numerics
SS 2010 Numerics for Mechanical Engineers
Numerics of Parabolic Equations
Bachelor/Master Seminar on Numerics
WS 2009/10 Introduction to Numerics
Numerics of Hyperbolic Equations
Bachelor/Master Seminar on Numerics
SS 2009 on sabbatical
WS 2008/09 Numerics for Engineers and Physicists
Proseminar: Proofs from THE BOOK
SS 2008 Numerics for Mechanical Engineers
Seminar Scientific Computing
WS 2007/08 Introduction to Numerics
Theory of ODEs/PDEs for Mechanical Engineers
Seminar Scientific Computing
SS 2007 Introduction to Mathematical Modelling
Numerics of Evolutionary Equations
WS 2006/07 Numerics of Elliptic PDEs
Seminar Scientific Computing
SS 2006 Numerics of ODEs
How to solve it?
WS 2005/06 Introduction to Numerics
Seminar Scientific Computing
Seminar Mathematical Modelling
SS 2005 on sabbatical
WS 2004/05 Seminar Scientific Computing
Seminar Mathematical Modelling
Numerics for Information Scientists/CE
SS 2004 Seminar: A Posteriori Error Estimates
Numerics for Mechanical Engineers
WS 2003/04 Numerics of Stiff Differential Equations
Seminar Mathematical Modelling
SS 2003 Numerics of Parabolic and Hyperbolic PDEs
Modelling and Solving Practical Problems
WS 2002/03 Numerics of Elliptic PDEs
Seminar Mathematical Modelling
SS 2002 Numerics of ODEs
Modelling and Solving Practical Problems
WS 2001/02 Introduction to Numerics
Seminar Mathematical Modelling
Potsdam Institute for Climate Impact Research
SS 2000 Introduction to Numerics of PDEs
Martin-Luther University Halle-Wittenberg
WS 2000/01 Numerics I
Adaptive Solution of Parabolic Differential Equations
Seminar Numerics of Differential Equations
Berlin University of Technology
WS 1999/00 Numerics for Computer Scientists
Free University Berlin
SS 2001 Theory and Numerics of DAEs
Introduction to Numerics of PDEs
Introduction to Numerics of ODEs
WS 2000/01 Theory and Numerics of Reaction-Diffusion-Equations
SS 1999 Is Fluid Dynamics Predictable?
WS 1997/98 Numerics of PDEs: Bases of Functional Analysis
Numerics of PDEs: Programming and Simulation
SS 1997 Numerics of PDEs: Reaction-Diffusion-Systems and FEM
WS 1996/97 Introduction to Numerics of PDEs

KARDOS

Software Package for Solving Non-linear Evolution Problems

Copyright (C) 1997-2001 ZIB Berlin. All rights reserved.

Copyright (C) 2001-2023 Prof. Lang & ZIB Berlin. All rights reserved.

The code KARDOS was originally developed at ZIB Berlin to solve systems of non-linear mixed parabolic-elliptic partial differential equations by means of adaptive space and time discretizations. Linearly implicit one-step methods of Rosenbrock type are coupled with standard Finite Elements of various orders. KARDOS uses unstructured grids in one, two, and three space dimensions.

A large proportion of the current work is carried out in close collaboration with ZIB Berlin. Extensions that we are working on include: incorporation of computational fluid dynamics (CFD), optimisation and moving finite elements.

An older one-dimensional version of KARDOS can be downloaded. More informations on what type of problems can be solved and how to work with KARDOS are provided in the KARDOS User's Guide (appeared as report ZR-02-42 of ZIB Berlin).

Although this software is mainly used for scientific and educational purposes, we are interested in coorperations with external organisations (industry, goverment research laboratories, etc) or other university departments (particularly engineering departments).


University Education
1999 Habilitation in Mathematics, Freie Universität Berlin
1988 Dissertation (Dr. rer. nat) in Mathematics, Martin-Luther-Universität Halle-Wittenberg
1986 Diploma Degree Mathematics, Martin-Luther-Universität Halle-Wittenberg
1984 – 1985 Studied Mathematical Physics, State University of St. Petersburg, Russia
1981 – 1986 Studied Mathematics, Martin-Luther-Universität Halle-Wittenberg

Professional Experience
2025 Visiting University of Michigan, Ann Arbor, US
2022 Visiting University of Pennsylvania, Philadelphia, US
2017, 2025 Visiting University of Southern Denmark, Odense
2014 – 2016 Dean, Department of Mathematics, Technische Universität Darmstadt
2009, 2013 Visiting CWI, Amsterdam, The Netherlands
2008 Visiting The University of Auckland, New Zealand
2008, 2012 Visiting The University of Kansas, Lawrence, Kansas, US
2005
Visiting CWI, Amsterdam, The Netherlands
since 2001 Professor (C4/W3) at Technische Universität Darmstadt, Department of Mathematics
2000 – 2001 Acting as Professor at Martin-Luther-Universität Halle-Wittenberg
1999 Visiting Simon Fraser University, Vancouver B.C., Canada
1999 – 2001 Private Lecturer, Freie Universität Berlin
1994 – 2001 Research Scientist of Scientific Software Group, Zuse-Institute Berlin
1990 – 1994 PostDoc, Zuse-Institute Berlin
1988 – 1990 Assistant Lecturer, Research Follow, Martin-Luther-Universität Halle-Wittenberg

Professional Activities
2014 – 2018 Vice Spokesperson of Collaborative Research Center SFB/Transregio 154
2007 – 2019 Principal Investigator and Vice Dean for Ph.D. Studies at Excellence Graduate School of Computational Engineering, Technische Universität Darmstadt
2006 – 2022 Editor of Applied Numerical Mathematics (Elsevier)

Awards, Honors and Offers
2019 Berlin Research Award for Alternatives to Animal Experiments
2006 Offer for Full Professorship at Technische Universität Chemnitz
2001 Offer for Full Professorship at Technische Universität Darmstadt
1985 Ph.D. Research Grant, Martin-Luther-Universität Halle-Wittenberg
1984 – 1985 Student Award, Martin-Luther-Universität Halle-Wittenberg

Future Energy Systems

Thermo-Fluids & Interfaces

SFB/TRR154: Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks, 2014-2026

SFB/TRR146: Multiscale Simulation Methods for Soft-Matter Systems, 2014-2026

Darmstadt Graduate School of Excellence Energy Science and Engineering, 2012-2018

Darmstadt Graduate School of Excellence Computational Engineering, 2012-2018