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
American Mathematical Monthly
American Mathematical Monthly
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
On the Gibbs Phenomenon and Its Resolution
SIAM Review
High-Order Central Schemes for Hyperbolic Systems of Conservation Laws
SIAM Journal on Scientific Computing
Journal of Computational Physics
Comparison of several spatial discretizations for the Navier-Stokes equations
Journal of Computational Physics
A technique of treating negative weights in WENO schemes
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Finite-volume WENO schemes for three-dimensional conservation laws
Journal of Computational Physics
Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points
Journal of Computational Physics
A Weighted Essentially Nonoscillatory, Large Time-Step Scheme for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Journal of Computational Physics
An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws
Journal of Computational Physics
Hierarchical reconstruction for spectral volume method on unstructured grids
Journal of Computational Physics
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics
Positivity-preserving high order finite difference WENO schemes for compressible Euler equations
Journal of Computational Physics
Representation of the Lagrange reconstructing polynomial by combination of substencils
Journal of Computational and Applied Mathematics
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The reconstruction approach [C.W. Shu, High-order weno schemes for convection-dominated problems, SIAM Rev. 51 (1) (2009) 82-126] for the numerical approximation of f^'(x) is based on the construction of a dual function h(x) whose sliding averages over the interval [x-12@Dx,x+12@Dx] are equal to f(x) (assuming a homogeneous grid of cell-size @Dx). We study the deconvolution problem [A. Harten, B. Engquist, S. Osher, S.R. Chakravarthy, Uniformly high-order accurate essentially nonoscillatory schemes III, J. Comput. Phys. 71 (1987) 231-303] which relates the Taylor-polynomials of h(x) and f(x), and obtain its explicit solution, by introducing rational numbers @t"n defined by a recurrence relation, or determined by their generating function, g"@t(x), related with the reconstruction pair of e^x. We then apply these results to the specific case of Lagrange-interpolation-based polynomial reconstruction, and determine explicitly the approximation error of the Lagrange reconstructing polynomial (whose sliding averages are equal to the Lagrange interpolating polynomial) on an arbitrary stencil defined on a homogeneous grid.