Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Essentially Non-Oscillatory Adaptive Tree Methods
Journal of Scientific Computing
High Order Finite Difference WENO Schemes for Nonlinear Degenerate Parabolic Equations
SIAM Journal on Scientific Computing
Applied Numerical Mathematics
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Shu and Osher introduced a conservative finite difference discretization for hyperbolic conservation laws using nodal values rather than the traditional cell averages. Their form was obtained by introducing mathematical relations that simplify the resulting numerical methods. Here we instead “derive” their form from the standard cell average approach. In the process, we clarify the origin of their relations and the properties of this formulation. We also investigate the extension of their form to non-uniform grids. We show the strict conservation form only extends to grids with quadratic or exponential stretching. However, a slight generalization can be applied to all smoothly stretched grids with no loss of essential properties.