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- Alexander Kurganov, Sebastian Noelle, Guergana Petrova
- SIAM J. Scientific Computing
- 2001

We introduce new Godunov-type semidiscrete central schemes for hyperbolic systems of conservation laws and Hamiltonâ€“Jacobi equations. The schemes are based on the use of more precise informationâ€¦ (More)

A family of Godunov-type central-upwind schemes for the Saint-Venant system of shallow water equations has been first introduced in [A. Kurganov and D. Levy, M2AN Math. Model. Numer. Anal., 36â€¦ (More)

- Peter Binev, Albert Cohen, Wolfgang Dahmen, Ronald A. DeVore, Guergana Petrova, Przemyslaw Wojtaszczyk
- SIAM J. Math. Analysis
- 2011

The reduced basis method was introduced for the accurate online evaluation of solutions to a parameter dependent family of elliptic partial differential equations. Abstractly, it can be viewed asâ€¦ (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 semidiscrete central-upwindâ€¦ (More)

Given a Banach space X and one of its compact sets F , we consider the problem of finding a good n dimensional space Xn âŠ‚ X which can be used to approximate the elements of F . The best possibleâ€¦ (More)

- Alexander Kurganov, Guergana Petrova
- SIAM J. Scientific Computing
- 2009

We derive a second-order semi-discrete central-upwind scheme for oneand two-dimensional systems of two-layer shallow water equations. We prove that the presented scheme is wellbalanced in the senseâ€¦ (More)

We present a family of central-upwind schemes on general triangular grids for solving two-dimensional systems of conservation laws. The new schemes enjoy the main advantages of the Godunov-typeâ€¦ (More)

- Alexander Kurganov, Guergana Petrova
- Numerische Mathematik
- 2001

We construct a new third-order semi-discrete genuinely multidimensional central scheme for systems of conservation laws and related convection-diffusion equations. This construction is based onâ€¦ (More)

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-upwindâ€¦ (More)

- B Otero, Lubomira A. Dontcheva, +4 authors Charles R. Doering
- 2004

By JESSE OTERO, LUBOMIRA A. DONTCHEVA, HANS JOHNSTON, RODNEY A. WORTHING, ALEXANDER KURGANOV, GUERGANA PETROVA AND CHARLES R. DOERING 3,7 Department of Mathematics, Ohio State University, Columbus,â€¦ (More)