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or perhaps with a forcing term g(u, x, t) on the right-hand side. Here u 5 (u1 , ..., um), f 5 (f1 , ..., fd), x 5 (x1 , ..., xd) In this paper, we further analyze, test, modify, and improve the high order WENO (weighted essentially non-oscillatory) finite differand t . 0. ence schemes of Liu, Osher, and Chan. It was shown by Liu et al. WENO schemes are… (More)

- Guang-Shan Jiang, Danping Peng
- SIAM J. Scientific Computing
- 2000

In this paper, we present a weighted ENO (essentially non-oscillatory) scheme to approximate the viscosity solution of the Hamilton-Jacobi equation: = 0: This weighted ENO scheme is constructed upon and has the same stencil nodes as the 3 rd order ENO scheme but can be as high as 5 th order accurate in the smooth part of the solution. In addition to the… (More)

- Guang-Shan Jiang, Eitan Tadmor
- SIAM J. Scientific Computing
- 1998

We construct, analyze, and implement a new nonoscillatory high-resolution scheme for two-dimensional hyperbolic conservation laws. The scheme is a predictor-corrector method which consists of two steps: starting with given cell averages, we first predict pointvalues which are based on nonoscillatory piecewise-linear reconstructions from the given cell… (More)

In this paper, we further analyze, test, modify and improve the high order WENO (weighted essentially non-oscillatory) nite di erence schemes of Liu, Osher and Chan [9]. It was shown by Liu et al. that WENO schemes constructed from the r order (in L norm) ENO schemes are (r+1) order accurate. We propose a new way of measuring the smoothness of a numerical… (More)

Numerical simulations often provide strong evidences for the existence and stability of discrete shocks for certain nite diierence schemes approximating conservation laws. This paper presents a framework for converting such numerical observations to mathematical proofs. The framework is applicable to conservative schemes approximating stationary shocks of… (More)

- Guang-Shan Jiang
- 1996

In this paper, we further analyze, test, modify and improve the high order WENO (weighted essentially non-oscillatory) nite diierence schemes of Liu, Osher and Chan 9]. It was shown by Liu et al. that WENO schemes constructed from the r th order (in L 1 norm) ENO schemes are (r +1) th order accurate. We propose a new way of measuring the smoothness of a… (More)

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