Now showing items 1-12 of 12

  • Chatterjee, Neelabja; Fjordholm, Ulrik Skre (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2018)
    We derive and study a Lax–Friedrichs-type finite volume method for a large class of nonlocal continuity equations in multiple dimensions. We prove that the method converges weakly to the measure-valued solution and converges ...
  • Solem, Susanne; Fjordholm, Ulrik Skre; Carrillo, José A (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2020)
    Inspired by so-called TVD limiter-based second-order schemes for hyperbolic conservation laws, we develop a formally second-order accurate numerical method for multi-dimensional aggregation equations. The method allows for ...
  • Chatterjee, Neelabja; Fjordholm, Ulrik Skre (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2020)
    High-order accurate, entropy stable numerical methods for hyperbolic conservation laws have attracted much interest over the last decade, but only a few rigorous convergence results are available, particularly in multiple ...
  • Fjordholm, Ulrik Skre; Lye, Kjetil Olsen (Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2022)
    We prove convergence rates of monotone schemes for conservation laws for Hölder continuous initial data with unbounded total variation, provided that the Hölder exponent of the initial data is greater than 12/. For strictly ...
  • Fjordholm, Ulrik Skre; Lye, Kjetil; Mishra, Siddhartha (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2018)
    We propose efficient numerical algorithms for approximating statistical solutions of scalar conservation laws. The proposed algorithms combine finite volume spatio-temporal approximations with Monte Carlo and multilevel ...
  • Fjordholm, Ulrik Skre; Ruf, Adrian Montgomery (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2021)
    We present a second-order accurate numerical method for a class of nonlocal nonlinear conservation laws called the “nonlocal pair-interaction model,” which was recently introduced by Du, Huang, and LeFloch [SIAM J. Numer. ...
  • Fjordholm, Ulrik Skre (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2018)
    We give two conditions that are necessary and sufficient for the uniqueness of Filippov solutions to scalar, autonomous ordinary differential equations with discontinuous velocity fields. When only one of the two conditions ...
  • Fjordholm, Ulrik Skre; Wiedemann, Emil (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2017)
    We prove a version of Onsager’s conjecture on the conservation of energy for the incompressible Euler equations in the context of statistical solutions, as introduced recently by Fjordholm et al. (2017). As a byproduct, ...
  • Fjordholm, Ulrik Skre; Lye, Kjetil; Mishra, Siddhartha; Weber, Franziska (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2020)
    Statistical solutions are time-parameterized probability measures on spaces of integrable functions, which have been proposed recently as a framework for global solutions and uncertainty quantification for multi-dimensional ...
  • Fjordholm, Ulrik Skre (Master thesis / Masteroppgave, 2009)
  • Fjordholm, Ulrik Skre; Musch, Markus; Risebro, Nils Henrik (Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2022)
    We continue the analysis of nonlinear conservation laws on networks initiated in [M. Musch, U. S. Fjordholm, and N. H. Risebro, Netw. Heterog. Media, 17 (2022), pp. 101--128] by extending our analysis to a large class of ...
  • Musch, Markus; Fjordholm, Ulrik Skre; Risebro, Nils Henrik (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2022)
    We consider nonlinear scalar conservation laws posed on a network. We define an entropy condition for scalar conservation laws on networks and establish $L^1$ stability, and thus uniqueness, for weak solutions satisfying ...