Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Uniformly high-order accurate nonoscillatory schemes
SIAM Journal on Numerical Analysis
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Journal of Computational Physics
Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points
Journal of Computational Physics
An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws
Journal of Computational Physics
Some results on uniformly high-order accurate essentially nonoscillatory schemes
Applied Numerical Mathematics
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics
ENO schemes with subcell resolution
Journal of Computational Physics
High order weighted essentially non-oscillatory WENO-Z schemes for hyperbolic conservation laws
Journal of Computational Physics
Analysis of WENO Schemes for Full and Global Accuracy
SIAM Journal on Numerical Analysis
Spectral analysis of nonlinear finite difference discretizations
Journal of Computational and Applied Mathematics
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The weighted essentially non-oscillatory (WENO) methods are a popular high-order spatial discretization for hyperbolic partial differential equations. Recently Henrick et al. (J. Comput. Phys. 207:542---567, 2005) noted that the fifth-order WENO method by Jiang and Shu (J. Comput. Phys. 126:202---228, 1996) is only third-order accurate near critical points of the smooth regions in general. Using a simple mapping function to the original weights in Jiang and Shu (J. Comput. Phys. 126:202---228, 1996), Henrick et al. developed a mapped WENO method to achieve the optimal order of accuracy near critical points. In this paper we study the mapped WENO scheme and find that, when it is used for solving the problems with discontinuities, the mapping function in Henrick et al. (J. Comput. Phys. 207:542---567, 2005) may amplify the effect from the non-smooth stencils and thus cause a potential loss of accuracy near discontinuities. This effect may be difficult to be observed for the fifth-order WENO method unless a long time simulation is desired. However, if the mapping function is applied to seventh-order WENO methods (Balsara and Shu in J. Comput. Phys. 160:405---452, 2000), the error can increase much faster so that it can be observed with a moderate output time. In this paper a new mapping function is proposed to overcome this potential loss of accuracy.