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
Official home page http://www.mn.uio.no/math/english/people/aca/ulriksf/index.html
Ulrik Skre Fjordholm

Publications

Pre/post prints

U. S. Fjordholm and E. Wiedemann.
Statistical solutions and Onsager's conjecture.
Physica D, to appear, 2018.
[errata] [arXiv] [doi]
J. A. Carrillo, U. S. Fjordholm and S. Solem.
A second-order numerical method for the aggregation equations.
Submitted for publication, 2018.
[arXiv]
U. S. Fjordholm.
Sharp uniqueness conditions for one-dimensional, autonomous ordinary differential equations.
Submitted for publication, 2018.
[arXiv]
N. Chatterjee and U. S. Fjordholm.
A convergent finite volume method for the Kuramoto equation and related non-local conservation laws.
Submitted for publication, 2018.
[arXiv]
U. S. Fjordholm, S. Mishra and K. O. Lye.
Numerical approximation of statistical solutions of scalar conservation laws.
Submitted for publication, 2017.
[arXiv]

Book chapters

U. S. Fjordholm.
Stability properties of the ENO method.
In Handbook of Numerical Methods for Hyperbolic Problems: Basic and Fundamental Issues, volume 17 of Handbook of Numerical Analysis, page 123–145. 2016.
[errata] [arXiv] [doi] [bibtex]

Publications in journals

[13] U. S. Fjordholm, R. Käppeli, S. Mishra and E. Tadmor.
Construction of approximate entropy measure valued solutions for hyperbolic systems of conservation laws.
Found. Comput. Math., 17(3):763–827, 2017.
[arXiv] [doi] [bibtex]
[12] U. S. Fjordholm, S. Lanthaler and S. Mishra.
Statistical solutions of hyperbolic conservation laws I: Foundations.
Arch. Ration. Mech. An., 226(2):809–849, 2017.
[arXiv] [doi] [bibtex]
[11] U. S. Fjordholm and D. Ray.
A sign preserving WENO reconstruction method.
J. Sci. Comput., 68(1):42–63, 2016.
[arXiv] [doi] [bibtex]
[10] U. S. Fjordholm and S. H. Zakerzadeh.
High-order accurate, fully discrete entropy stable schemes for scalar conservation laws.
IMA J. Numer. Anal., 36(2):633–654, 2016.
[doi] [bibtex]
[9] U. S. Fjordholm, S. Mishra and E. Tadmor.
On the computation of measure-valued solutions.
Acta Numer., 25:567–679, 2016.
[doi] [bibtex]
[8] P. Chandrashekar, U. S. Fjordholm, S. Mishra and D. Ray.
Entropy stable schemes on two-dimensional unstructured grids.
Commun. Comput. Phys., 19(5):1111–1140, 2016.
[doi] [bibtex]
[7] U. S. Fjordholm and S. Solem.
Second-order convergence of monotone schemes for conservation laws.
SIAM J. Numer. Anal., 54(3):1920–1945, 2016.
[arXiv] [doi] [bibtex]
[6] U. S. Fjordholm, S. Mishra and E. Tadmor.
ENO Reconstruction and ENO Interpolation Are Stable.
Found. Comput. Math., 13(2):139–159, 2013.
[errata] [arXiv] [doi] [bibtex]
[5] M. J. Castro, U. S. Fjordholm, S. Mishra and C. Parés.
Entropy conservative and entropy stable schemes for non-conservative hyperbolic systems.
SIAM J. Numer. Anal., 51(3):1371–1391, 2013.
[doi] [bibtex]
[4] 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(2):544–573, 2012.
[doi] [bibtex]
[3] U. S. Fjordholm and S. Mishra.
Accurate numerical discretizations of non-conservative hyperbolic systems.
M2AN, 46(1):187–206, 2012.
[doi] [bibtex]
[2] U. S. Fjordholm, S. Mishra and E. Tadmor.
Well-balanced and energy stable schemes for the shallow water equations with discontinuous topography.
J. Comput. Phys., 230(14):5587–5609, 2011.
[doi] [bibtex]
[1] U. S. Fjordholm and S. Mishra.
Vorticity preserving finite volume schemes for the shallow water equations.
SIAM J. Sci. Comput., 33(2):588–611, 2011.
[doi] [bibtex]

Publications in conference proceedings

[3] U. S. Fjordholm.
Energy conservative and stable schemes for the two-layer shallow water equations.
In Hyperbolic Problems. Theory, Numerics and Applications, volume 18 of Series in Contemporary Applied Mathematics, page 414–421. 2012.
[doi] [bibtex]
[2] U. S. Fjordholm, S. Mishra and E. Tadmor.
Entropy Stable ENO Scheme.
In Hyperbolic Problems. Theory, Numerics and Applications, volume 17 of Series in Contemporary Applied Mathematics, page 12–27. 2012.
[doi] [pdf] [bibtex]
[1] U. S. Fjordholm, S. Mishra and E. Tadmor.
Energy preserving and energy stable schemes for the shallow water equations.
In Foundations of Computational Mathematics, Hong Kong 2008, volume 363 of London Math. Soc. Lecture Notes Series, page 93–139. 2009.
[doi] [pdf] [bibtex]

Theses

U. S. Fjordholm.
High-order accurate entropy stable numerical schemes for hyperbolic conservation laws.
PhD thesis, ETH Zürich, 2013.
[doi] [bibtex]
U. S. Fjordholm.
Structure preserving finite volume methods for the shallow water equations.
Master's thesis, University of Oslo, 2009.
[pdf] [bibtex]

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 2 May 2018.