Ulrik Skre Fjordholm

Associate professor
Department of Mathematics
University of Oslo

Postal address

Ulrik Skre Fjordholm
Department of Mathematics
University of Oslo
Postboks 1053 Blindern
0316 Oslo
Norway

Contact information

Visiting address Ullevål stadion, Sognsveien 77 B, 0855 Oslo
Email ulriksf (at) math.uio.no
Ulrik Skre Fjordholm

Publications

Submitted for publication/pending publication

U. S. Fjordholm, K. Lye and S. Mishra.
Numerical approximation of statistical solutions of scalar conservation laws.
Submitted for publication (2017). [arXiv]
U. S. Fjordholm and E. Wiedemann.
Statistical solutions and Onsager's conjecture.
Physica D (2017). [article] [arXiv]

Book chapters

U. S. Fjordholm.
Stability properties of the ENO method.
Handbook of Numerical Methods for Hyperbolic Problems: Basic and Fundamental Issues, Volume 17, pp. 123-145 (2016). [article] [arXiv] [errata]

Publications in journals

U. S. Fjordholm, S. Lanthaler and S. Mishra.
Statistical solutions of hyperbolic conservation laws I: Foundations.
Arch. Ration. Mech. Anal., 226(2), pp. 809-849 (2017). [article] [arXiv]
U. S. Fjordholm, R. Kaeppeli, S. Mishra and E. Tadmor.
Construction of approximate entropy measure valued solutions for hyperbolic systems of conservation laws.
Foundations of Computational Mathematics, 17 (3), pp. 763-827 (2017). [article] [arXiv]
U. S. Fjordholm and S. Solem.
Second-order convergence of monotone schemes for conservation laws.
SIAM J. Numer. Anal., 54(3), pp. 1920-1945 (2016). [article] [arXiv]
U. S. Fjordholm, S. Mishra and E. Tadmor.
On the computation of measure-valued solutions.
Acta Numerica, 25, pp. 567-679 (2016). [article]
U. S. Fjordholm and D. Ray.
A sign preserving WENO reconstruction method.
Journal of Scientific Computing, 68(1), pp. 42-63 (2016). [article] [arXiv]
U. S. Fjordholm and S. H. Zakerzadeh.
High-order accurate, fully discrete entropy stable schemes for scalar conservation laws.
IMA Journal of Numerical Analysis, 36 (2), pp. 633-654 (2016). [article]
P. Chandrashekar, U. S. Fjordholm, S. Mishra and D. Ray.
Entropy stable schemes on two-dimensional unstructured grids.
Communications in Computational Physics, 19, pp. 1111-1140 (2016). [article]
M. J. Castro, U. S. Fjordholm, S. Mishra and C. Pares.
Entropy conservative and entropy stable schemes for non-conservative hyperbolic systems.
SIAM J. Numer. Anal., 51(3), pp. 1371-1391 (2013). [article]
U. S. Fjordholm, S. Mishra and E. Tadmor.
ENO reconstruction and ENO interpolation are stable.
Foundations of Computational Mathematics, 13 (2), pp. 139-159 (2013). [article] [arXiv] [errata]
U. S. Fjordholm, S. Mishra and E. Tadmor.
Arbitrarily high order accurate entropy stable essentially non-oscillatory schemes for systems of conservation laws.
SIAM J. Numer. Anal., 50, pp. 544-573 (2012). [article]
U. S. Fjordholm and S. Mishra.
Accurate numerical discretizations of non-conservative hyperbolic systems.
M2AN, 46, pp. 187-206 (2011). [article]
U. S. Fjordholm and S. Mishra.
Vorticity preserving finite volume schemes for the shallow water equations.
SIAM J. Sci. Comput., 33, pp. 588-611 (2011). [article]
U. S. Fjordholm, S. Mishra and E. Tadmor.
Well-balanced and energy stable schemes for the shallow water equations with discontinuous topography.
Journal of Computational Physics, 230(14), pp. 5587-5609 (2011). [article]

Publications in conference proceedings

U. S. Fjordholm, S. Mishra and E. Tadmor.
Entropy stable ENO scheme.
"Hyperbolic Problems: Theory, Numerics, Applications", Proceedings of the 13th International Conference held in Beijing, June 2010 (T. Li & S. Jiang, eds.), vol 1, pp. 12-27 (2012). [technical report]
U. S. Fjordholm.
Energy conservative and -stable schemes for the two-layer shallow water equations.
"Hyperbolic Problems: Theory, Numerics, Applications", Proceedings of the 13th International Conference held in Beijing, June 2010 (T. Li & S. Jiang, eds.), vol 2, pp. 414-421 (2012). [technical report]
U. S. Fjordholm, S. Mishra and E. Tadmor.
Energy preserving and energy stable schemes for the shallow water equations.
In "Foundations of Computational Mathematics", Proc. FoCM held in Hong Kong 2008 (F. Cucker, A. Pinkus and M. Todd, eds), London Math. Soc. Lecture Notes Ser. (363), pp. 93-139 (2009). [article] [pdf]

Theses

Ph.D. thesis
High-order accurate entropy stable numerical schemes for hyperbolic conservation laws. ETH Zurich (February 2013). [doi]
Master thesis
Structure preserving finite volume methods for the shallow water equations. University of Oslo (June 2009). [pdf]

Software

Compack (Conservation law MATLAB package) is a MATLAB package for solving one- and two-dimensional systems of conservation law. It provides a simple interface to a set of solvers for a wide range of hyperbolic conservation laws, and is written in a modular fashion to ease the implementation of new solvers, models, source terms etc.


Last modified on 1 November 2017.