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- Jean-Luc Guermond, Richard Pasquetti, Bojan Popov
- J. Comput. Physics
- 2011

Keywords: Entropy viscosity Conservation laws Euler equations Finite elements Spectral elements Fourier method Godunov schemes Central schemes a b s t r a c t A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of… (More)

- Kirill Kopotun, Marian Neamtu, Bojan Popov
- Math. Comput.
- 2003

A new class of Godunov-type numerical methods for solving nonlinear scalar conservation laws in one space dimension is introduced. This new class of methods , called weakly non-oscillatory (WNO), is a generalization of the classical non-oscillatory schemes. Under certain conditions, convergence and error estimates for the methods are proved. Examples of… (More)

The T2K experiment has observed electron neutrino appearance in a muon neutrino beam produced 295 km from the Super-Kamiokande detector with a peak energy of 0.6 GeV. A total of 28 electron neutrino events were detected with an energy distribution consistent with an appearance signal, corresponding to a significance of 7.3σ when compared to 4.92±0.55… (More)

- Alexander Kurganov, Guergana Petrova, Bojan Popov
- SIAM J. Scientific Computing
- 2007

We discover that the choice of a piecewise polynomial reconstruction is crucial in computing solutions of nonconvex hyperbolic (systems of) conservation laws. Using semi-discrete central-upwind schemes we illustrate that the obtained numerical approximations may fail to converge to the unique entropy solution or the convergence may be so slow that achieving… (More)

The T2K experiment observes indications of ν(μ) → ν(e) appearance in data accumulated with 1.43×10(20) protons on target. Six events pass all selection criteria at the far detector. In a three-flavor neutrino oscillation scenario with |Δm(23)(2)| = 2.4×10(-3) eV(2), sin(2)2θ(23) = 1 and sin(2)2θ(13) = 0, the expected number of such events is 1.5±0.3(syst).… (More)

- Jean-Luc Guermond, Bojan Popov
- Numerische Mathematik
- 2008

A new approximation technique based on L 1-minimization is introduced. It is proven that the approximate solution converges to the viscosity solution in the case of one-dimensional stationary Hamilton-Jacobi equation with convex Hamiltonian.

- Ivan Christov, Bojan Popov
- J. Comput. Physics
- 2008

We discuss an extension of the Jiang–Tadmor and Kurganov–Tadmor fully-discrete non-oscillatory central schemes for hyperbolic systems of conservation laws to unstructured triangular meshes. In doing so, we propose a new, ''genuinely multidimensional, " non-oscillatory reconstruction—the minimum-angle plane reconstruction (MAPR). The MAPR is based on the… (More)

- Jean-Luc Guermond, Richard Pasquetti, Bojan Popov
- J. Sci. Comput.
- 2011

This paper focuses on the notion of suitable weak solutions for the three-dimensional incompressible Navier–Stokes equations and discusses the relevance of this notion to Computational Fluid Dynamics. The purpose of the paper is twofold (i) to recall basic mathematical properties of the three-dimensional in-compressible Navier-Stokes equations and to show… (More)

- Jean-Luc Guermond, Murtazo Nazarov, Bojan Popov, Yong Yang
- SIAM J. Numerical Analysis
- 2014

This paper proposes an explicit, (at least) second-order, maximum principle satisfying , Lagrange finite element method for solving nonlinear scalar conservation equations. The technique is based on a new viscous bilinear form introduced in Guermond and Nazarov [Com-put. a high-order entropy viscosity method, and the Boris–Book–Zalesak flux correction… (More)

- Y. Efendiev, B. Popov
- 2005

In this paper we study homogenization of nonlinear hyperbolic equations. The weak limit of the solutions is investigated by approximating the flux functions with piecewise linear functions. We study mostly Riemann problems for layered velocity fields as well as for the heterogeneous divergence free velocity fields. 1. Introduction. The homogenization of… (More)