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Jan Nordström

Professor Emeritus

Time-dependent partial differential equations

I develop numerical methodology for multi-physics applications governed by partial differential equations. My main interest is in initial boundary value problems, and in particular the fundamental effect of boundary and interface conditions on well-posedness and stability.

Find me on ResearchGate

Professional activities

Professional activities

  • Associate editor of Journal of Computational Physics (JCP), Elsevier
  • Associate editor of BIT Numerical Mathematics, Springer Verlag

Affiliations

  • Senior Visiting Fellow, Center for Turbulence Research, Stanford University, USA, 2005-2007
  • Senior Research Fellow, Center for Turbulence Research, Stanford University, USA, 2009-2010
  • Honorary Professor, School of Computational and Applied Mathematics, University of the Witwatersrand, South Africa, 2010-2013
  • Honorary Professor, Department of Mechanical Engineering, Faculty of Engineering and the Built Environment, University of Cape Town, South Africa, 2018-2023
  • Distinguished Visiting Professor, Department of Mathematics and Applied Mathematics, University of Johannesburg, South Africa, 2020-2025
  • Honorary Professor, Department of Mechanical Engineering, Faculty of Engineering and the Built Environment, University of Cape Town, South Africa, 2025-2030
  • Distinguished Visiting Professor, Department of Mathematics and Applied Mathematics, University of Johannesburg, South Africa, 2025-2030

Research networks

  • Member of Academy of Science of South Africa (ASSAf)
  • Member of SAMS (South African Mathematical Society)

Teaching

  • Project course in computational mathematics, 12 hp, autumn 2024, Linköping University
  • Project course in computational mathematics, 12 hp, autumn 2023, Linköping University
  • Combining Partial Differential Equations, Machine Learning and Measurements for Increased Prediction Capability, 3 hp, autumn 2019, Linköping University
  • Numerical Solution of Initial Boundary Value Problems (MAI0122), 3 hp, autumn 2017, Linköping University, and University of Cape Town, South Africa
  • Stochastic Galerkin Methods for Partial Differential Equations (MAI0129), 5 hp, spring 2016, Linköping University
  • Selected articles on well posed problems and numerical approximation, 5 hp, autumn 2014, Linköping University
  • Numerical Solution of Initial Boundary Value Problems (MAI0122), 3 hp, autumn 2013, Linköping University
  • Short course: Numerical Methods for Initial Boundary Value Problems, spring 2013, Council for Scientific and Industrial Research (CSIR) in South Africa
  • Numerical Methods for Initial Boundary Value Problems (MAI0106), autumn 2011, Linköping University
  • Numerical Methods for Initial Boundary Value Problems (CME 326), spring 2011, Stanford University
  • Numerical Methods for Initial Boundary Value Problems (CME 326), winter 2009, Stanford University 

CV

Research

Numerical Solutions of Time-Dependent Partial Differential Equations

Well-posedness of the governing partial differential equations lead to effective and accurate numerical methods for the analysis of physical processes in science and engineering.

News

MAI researcher elected to Academy of Science of South Africa

Professor Emeritus Jan Nordström, at the Department of Mathematics (MAI), has been elected to membership of the Academy of Science of South Africa (ASSAf).
Three students walking in Campus Valla

International four-way collaboration ready to start

An unique four-way collaboration project will enable 21 Students from Linköping University and 21 Washington State University to participate in an innovative exchange and research programme in engineering science and scientific computation.
Per Eklund in the lab.

64 million SEK for research in the natural sciences and technology

Seventeen researchers working in technology and the natural sciences at Linköping University have been awarded 64 million Swedish kronor in the form of research grants from the Swedish Research Council.

Former PhD students

  • Fredrik Laurén. Thesis title: Summation-by-parts formulations for flow problems 2017-2022. Link to thesis.
  • Oskar Ålund. Thesis title: Applications of summation-by-parts operators 2016-2021. Link to thesis.
  • Andrea Alessandro Ruggiu. Thesis title: Eigenvalue analysis and convergence acceleration techniques for summation-by-parts approximations, 2014-2019. Link to thesis.
  • Fatemeh Ghasemi Zinatabadi. Thesis title: Stability, dual consistency and conservation of summation-by-parts formulations for multiphysics problems, 2014-2019. Link to thesis.
  • Markus Wahlsten. Thesis title: Uncertainty quantification for wave propagation and flow problems with random data, 2013-2018. Link to thesis.
  • Viktor Linders. Thesis title: Error analysis of summation-by-parts formulations: Dispersion, transmission and accuracy, 2012-2017. Link to thesis.
  • Cristina La Cognata. Thesis title: High order summation-by-parts based approximations for discontinuous and nonlinear problems, 2012-2017. Link to thesis.
  • Hannes Frenander. Thesis title: High-order finite difference approximations for hyperbolic problems: multiple penalties and non-reflecting boundary conditions, 2012-2017. Link to thesis.
  • Ossian O'Reilly. Thesis title: Numerical methods for wave propagation in solids containing faults and fluid-filled fractures, (jointly with Eric Dunham Stanford University), 2011-2016. Link to thesis.
  • Samira Nikkar. Thesis title: Stable High Order Finite Difference Methods for Wave Propagation and Flow Problems on Deforming Domains, 2011-2016. Link to thesis.
  • Tomas Lundquist. Thesis title: High order summation-by-parts methods in time and space, 2011-2016. Link to thesis.
  • Per Pettersson. Thesis title: Uncertainty Quantification and Numerical Methods for Conservation Laws, (jointly with Gianluca Iaccarino, Stanford University), 2008-2013. Link to thesis at Uppsala University and Link to thesis at Stanford University.
  • Jens Berg. Thesis title: Stable and High-Order Finite Difference Methods for Multiphysics Flow Problems, 2008-2013. Link to thesis.
  • Kenneth Duru. Thesis title: Perfectly Matched Layers and High Order Difference Methods for Wave Equations, (Gunilla Kreiss, Uppsala University, 1st advisor), 2007-2012. Link to thesis.
  • Sofia Eriksson. Thesis title: Stable Numerical Methods with Boundary and Interface Treatment for Applications in Aerodynamics, 2007-2012. Link to thesis.
  • Sven-Erik Ekström. Thesis title (Lic): A Vertex-Centered Discontinuous Galerkin Method for Flow Problems, (Martin Berggren, Umeå University, 1st advisor), 2006-2016. Link to thesis.
  • Qaiser Abbas. Thesis title: Weak Boundary and Interface Procedures for Wave and Flow Problems, 2006-2011. Link to thesis.
  • Jing Gong. Thesis title: Hybrid Methods for Unsteady Fluid Flow Problems in Complex Geometries, 2003-2007. Link to thesis.
  • Magnus Svärd. Thesis title: Stable High Order Finite Difference Methods for Aerodynamics, 1999-2004. Link to thesis.
  • Ken Mattsson. Thesis title: Summation-by-Parts Operators for High Order Finite Difference Methods, 1997-2003. Link to thesis.

Former postdoc

Marco Kupiainen. Project: IDIHOM, InDustrIalisation of Higher Order Methods, 2011-2014.

Publications

Publication list for Jan Nordström

2025

Hanifa Hanif, Jan Nordström, Arnaud. G. Malan (2025) Efficiency analysis of continuous and discontinuous Galerkin finite element methods AIMS Mathematics, Vol. 10, p. 22579-22597 (Article in journal) Continue to DOI
Prince Nchupang, Arnaud G. Malan, Jan Nordström (2025) A stable and accurate finite difference approximation for the incompressible lid-driven cavity flow with focus on the corner singularities Computers & Fluids, Vol. 302, Article 106826 (Article in journal) Continue to DOI
Charis Harley, Ebrahim Momoniat, Jan Nordström (2025) A Stable and Conservative Hybrid Scheme for the Frank-Kamenetskii Equation Journal of Scientific Computing, Vol. 103, Article 29 (Article in journal) Continue to DOI
Jan Nordström (2025) Open boundary conditions for nonlinear initial boundary value problems Journal of Computational Physics, Vol. 530, Article 113909 (Article in journal) Continue to DOI
Alexander Rothkopf, W.A. Horowitz, Jan Nordström (2025) Exact symmetry conservation and automatic mesh refinement in discrete initial boundary value problems Journal of Computational Physics, Vol. 524, Article 113686 (Article in journal) Continue to DOI
Jan Nordström, Arnaud G. Malan (2025) An Energy Stable Incompressible Multi-Phase Flow Formulation Journal of Computational Physics, Vol. 523, Article 113685 (Article in journal) Continue to DOI
David A. Kopriva, Andrew Ross Winters, Jan Nordström (2025) Energy Bounds for Discontinuous Galerkin Spectral Element Approximations of Well-Posed Overset Grid Problems for Hyperbolic Systems Journal of Computational Physics, Vol. 520, Article 113508 (Article in journal) Continue to DOI

2024

Craig Law, Jan Nordström (2024) Using Experimental Flow Visualisation Techniques to Interpret Computational Fluid Dynamics Data R & D Journal, Vol. 40, p. 10-16 (Article, review/survey) Continue to DOI
Jan Nordström, H. Collis, R. Brown, M. P. Nchupang, S. Mirjalili (2024) Toward energy-stable multi-phase flow schemes Proceedings of the Summer Program 2024 (Conference paper)
Craig Law, Jan Nordström (2024) Using experimental flow visualisation techniques to interpret computational fluid dynamics data Proceeding of the 13th South African Conference on Computational and Applied Mechanics, SACAM 2024, p. 131-141 (Conference paper)
Oskar Ålund, Yukinao Akamatsu, Fredrik Laurén, Takahiro Miura, Jan Nordström, Alexander Rothkopf (2024) Correction: Corrigendum to "Trace preserving quantum dynamics using a novel reparametrization-neutral summation-by-parts difference operator" [J.Comput.Phys. 425 (2021) 109917] Journal of Computational Physics, Vol. 519, Article 113517 (Article in journal) Continue to DOI
Alexander Rothkopf, Will Horowitz, Jan Nordström (2024) Exact space-time symmetry conservation and automatic mesh refinement for classical lattice field theory The 41st International Symposium on Lattice Field Theory (LATTICE2024) (Conference paper) Continue to DOI
Jan Nordström, Fredrik Laurén, Oskar Ålund (2024) An explicit Jacobian for Newton's method applied to nonlinear initial boundary value problems in summation-by-parts form AIMS Mathematics, Vol. 9, p. 23291-23312 (Article in journal) Continue to DOI
Jan Nordström (2024) A skew-symmetric energy stable almost dissipation free formulation of the compressible Navier-Stokes equations Journal of Computational Physics, Vol. 512, Article 113145 (Article in journal) Continue to DOI
Alexander Rothkopf, Jan Nordström (2024) The crucial role of Lagrange multipliers in a space-time symmetry preserving discretization scheme for IVPs Journal of Computational Physics, Vol. 511, Article 113138 (Article in journal) Continue to DOI
Jan Nordström (2024) Uncertain data in initial boundary value problems: Impact on short and long time predictions Journal of Computational Physics, Vol. 505, Article 112891 (Article in journal) Continue to DOI
Jan Glaubitz, Simon-Christian Klein, Jan Nordström, Philipp Öffner (2024) Summation-by-parts operators for general function spaces: The second derivative Journal of Computational Physics, Vol. 504, Article 112889 (Article in journal) Continue to DOI
Viktor Linders, Mark H. Carpenter, Jan Nordström (2024) A superconvergent stencil-adaptive SBP-SAT finite difference scheme Journal of Computational Physics, Vol. 501, Article 112794 (Article in journal) Continue to DOI
Jan Glaubitz, Jan Nordström, Philipp Öffner (2024) Energy-Stable Global Radial Basis Function Methods on Summation-By-Parts Form Journal of Scientific Computing, Vol. 98, Article 30 (Article in journal) Continue to DOI
Tomas Lundquist, Andrew Ross Winters, Jan Nordström (2024) Encapsulated generalized summation-by-parts formulations for curvilinear and non-conforming meshes Journal of Computational Physics, Vol. 498, Article 112699 (Article in journal) Continue to DOI
Alexander Rothkopf, Jan Nordström (2024) A symmetry and Noether charge preserving discretization of initial value problems Journal of Computational Physics, Vol. 498, Article 112652 (Article in journal) Continue to DOI
Jan Nordström (2024) Nonlinear Boundary Conditions for Initial Boundary Value Problems with Applications in Computational Fluid Dynamics Journal of Computational Physics, Vol. 498, Article 112685 (Article in journal) Continue to DOI

2023

Jan Glaubitz, Jan Nordström, Philipp Öffner (2023) Summation-by-Parts Operators for General Function Spaces SIAM Journal on Numerical Analysis, Vol. 61, p. 733-754 (Article in journal) Continue to DOI
Byron A. Jacobs, Fredrik Laurén, Jan Nordström (2023) On the order reduction of approximations of fractional derivatives: an explanation and a cure BIT Numerical Mathematics, Vol. 63, Article 17 (Article in journal) Continue to DOI
Jan Glaubitz, Simon-Christian Klein, Jan Nordström, Philipp Öffner (2023) Multi-dimensional summation-by-parts operators for general function spaces: Theory and construction Journal of Computational Physics, Vol. 491, Article 112370 (Article in journal) Continue to DOI
Irvy M. A. Gledhill, Hamed Roohani, Karl Forsberg, Peter Eliasson, Beric W. Skews, Jan Nordström (2023) Correction: Theoretical treatment of fluid flow for accelerating bodies (vol 30, pg 449, 2016) Theoretical and Computational Fluid Dynamics, Vol. 37, p. 129-129 (Article in journal) Continue to DOI
Remi Abgrall, Jan Nordström, Philipp Öffner, Svetlana Tokareva (2023) Analysis of the SBP-SAT Stabilization for Finite Element Methods Part II: Entropy Stability Communications on Applied Mathematics and Computation, Vol. 5, p. 573-595 (Article in journal) Continue to DOI
Alexander Rothkopf, Jan Nordström (2023) A new variational discretization technique for initial value problems bypassing governing equations Journal of Computational Physics, Vol. 477, Article 111942 (Article in journal) Continue to DOI
Tomas Lundquist, Arnaud G. Malan, Jan Nordström (2023) A Method-of-Lines Framework for Energy Stable Arbitrary Lagrangian-Eulerian Methods SIAM Journal on Numerical Analysis, Vol. 61, p. 2327-2351 (Article in journal) Continue to DOI
Mojalefa P. Nchupang, Arnaud G. Malan, Fredrik Laurén, Jan Nordström (2023) A provably stable and high-order accurate finite difference approximation for the incompressible boundary layer equations Computers & Fluids, Vol. 267, Article 106073 (Article in journal) Continue to DOI

Organisation

Fractal Plant

Department of Mathematics (MAI)

The department conducts research in computational mathematics, mathematics and applied mathematics, mathematical statistics, and optimization. We provide courses to students in most degree programmes in mathematics, science and engineering.
Illustrative picture representing mathematics

Applied Mathematics (TIMA)

Applied mathematics is used to study advanced methods for modeling in technology as well as natural and social sciences. The division conducts research in computational mathematics, mathematical statistics and optimization.

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