Time-dependent partial differential equations

In my research at Linköping University, we develop numerical methods for multi-physics applications governed by partial differential equations. We consider various kinds of uncertainties in the data or parameters of the problem and aim for a computational methodology that delivers an answer with error bars.

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Professional activities
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Professional activities

  • Head of Computational Mathematics at the Department of Mathematics
  • Member of the board of Linköping Institute of Technology (LiTH)
  • Member of the board of the National Supercomputer Centre in Sweden (NSC)
  • Associate editor of Journal of Computational Physics (JCP), Elsevier
  • Associate editor of BIT Numerical Mathematics, Springer Verlag


  • Senior Research Fellow, Center for Turbulence Research, Stanford University, USA, 2009 -
  • Honorary Professor, School of Computational and Applied Mathematics, University of the Witwatersrand, South Africa, 2010 -
  • Honorary Professor, Department of Mechanical Engineering, Faculty of Engineering and the Built Environment, University of Cape Town, South Africa, 2018 -

Research networks

  • Partner in the FP7 project UMRIDA (the European Union's Seventh Framework Programme, Uncertainty Management for Robust Industrial Design in Aeronautics)
  • Partner in the VINNOVA (Sweden's innovation agency) project MIAU
  • Member in SIAM (Society for Industrial and Applied Mathematics) and AIAA (The American Institute of Aeronautics and Astronautics)


  • 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 

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PhD students
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Former PhD students
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  • 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 och 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. 

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