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.
Jan Nordström
Professor Emeritus
Time-dependent partial differential equations
Professional activities
Professional activities
- Associate editor of AIMS Mathematics, AIMS Press
- 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 2025, Linköping University
- 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
News
Former PhD students
- Prince Nchupang. Thesis title: A Provably Stable and High-Order Accurate Finite Difference Approximation for the Incompressible Boundary Layer Equations, (A.G. Malan, University of Cape Town, 1st advisor), 2021-2024. Link to thesis.
- 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
2026
Aligning linear and nonlinear boundary condition theory for the compressible Euler equations using congruence matrix analysis
Journal of Computational Physics, Vol. 562, Article 115010
(Article in journal)
https://dx.doi.org/10.1016/j.jcp.2026.115010
Numerical boundary flux functions that give provable bounds for nonlinear initial boundary value problems with open boundaries
Journal of Computational Physics, Vol. 559, Article 114891
(Article in journal)
https://dx.doi.org/10.1016/j.jcp.2026.114891
Linear and Nonlinear Boundary Conditions: What's the difference?
Journal of Computational Physics, Vol. 550, Article 114649
(Article in journal)
https://dx.doi.org/10.1016/j.jcp.2025.114649
2025
An Optimization-Based Construction Procedure for Function Space-Based Summation-by-Parts Operators on Arbitrary Grids
Journal of Scientific Computing, Vol. 105, Article 83
(Article in journal)
https://dx.doi.org/10.1007/s10915-025-03062-1
Efficiency analysis of continuous and discontinuous Galerkin finite element methods
AIMS Mathematics, Vol. 10, p. 22579-22597
(Article in journal)
https://dx.doi.org/10.3934/math.20251005
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)
https://dx.doi.org/10.1016/j.compfluid.2025.106826
A Stable and Conservative Hybrid Scheme for the Frank-Kamenetskii Equation
Journal of Scientific Computing, Vol. 103, Article 29
(Article in journal)
https://dx.doi.org/10.1007/s10915-025-02854-9
Open boundary conditions for nonlinear initial boundary value problems
Journal of Computational Physics, Vol. 530, Article 113909
(Article in journal)
https://dx.doi.org/10.1016/j.jcp.2025.113909
Exact symmetry conservation and automatic mesh refinement in discrete initial boundary value problems
Journal of Computational Physics, Vol. 524, Article 113686
(Article in journal)
https://dx.doi.org/10.1016/j.jcp.2024.113686
An Energy Stable Incompressible Multi-Phase Flow Formulation
Journal of Computational Physics, Vol. 523, Article 113685
(Article in journal)
https://dx.doi.org/10.1016/j.jcp.2024.113685
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)
https://dx.doi.org/10.1016/j.jcp.2024.113508
2024
Using Experimental Flow Visualisation Techniques to Interpret Computational Fluid Dynamics Data
R & D Journal, Vol. 40, p. 10-16
(Article, review/survey)
https://dx.doi.org/10.69694/2309-8988/2024/v40a2
Toward energy-stable multi-phase flow schemes
Proceedings of the Summer Program 2024
(Conference paper)
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)
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)
https://dx.doi.org/10.1016/j.jcp.2024.113517
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)
https://dx.doi.org/10.22323/1.466.0353
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)
https://dx.doi.org/10.3934/math.20241132
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)
https://dx.doi.org/10.1016/j.jcp.2024.113145
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)
https://dx.doi.org/10.1016/j.jcp.2024.113138
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)
https://dx.doi.org/10.1016/j.jcp.2024.112891
Summation-by-parts operators for general function spaces: The second derivative
Journal of Computational Physics, Vol. 504, Article 112889
(Article in journal)
https://dx.doi.org/10.1016/j.jcp.2024.112889
A superconvergent stencil-adaptive SBP-SAT finite difference scheme
Journal of Computational Physics, Vol. 501, Article 112794
(Article in journal)
https://dx.doi.org/10.1016/j.jcp.2024.112794
Energy-Stable Global Radial Basis Function Methods on Summation-By-Parts Form
Journal of Scientific Computing, Vol. 98, Article 30
(Article in journal)
https://dx.doi.org/10.1007/s10915-023-02427-8
Encapsulated generalized summation-by-parts formulations for curvilinear and non-conforming meshes
Journal of Computational Physics, Vol. 498, Article 112699
(Article in journal)
https://dx.doi.org/10.1016/j.jcp.2023.112699
A symmetry and Noether charge preserving discretization of initial value problems
Journal of Computational Physics, Vol. 498, Article 112652
(Article in journal)
https://dx.doi.org/10.1016/j.jcp.2023.112652
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)
https://dx.doi.org/10.1016/j.jcp.2023.112685
2023
Summation-by-Parts Operators for General Function Spaces
SIAM Journal on Numerical Analysis, Vol. 61, p. 733-754
(Article in journal)
https://dx.doi.org/10.1137/22m1470141
On the order reduction of approximations of fractional derivatives: an explanation and a cure
BIT Numerical Mathematics, Vol. 63, Article 17
(Article in journal)
https://dx.doi.org/10.1007/s10543-023-00961-3
Multi-dimensional summation-by-parts operators for general function spaces: Theory and construction
Journal of Computational Physics, Vol. 491, Article 112370
(Article in journal)
https://dx.doi.org/10.1016/j.jcp.2023.112370
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)
https://dx.doi.org/10.1007/s00162-023-00639-0