ENO reconstruction and ENO interpolation are stable

Abstract

We prove stability estimates for the ENO reconstruction and ENO interpolation procedures. In particular, we show that the jump of the reconstructed ENO pointvalues at each cell interface has the same sign as the jump of the underlying cell averages across that interface. We also prove that the jump of the reconstructed values can be upper-bounded in terms of the jump of the underlying cell averages. Similar sign properties hold for the ENO interpolation procedure. These estimates, which are shown to hold for ENO reconstruction and interpolation of arbitrary order of accuracy and on non-uniform meshes, indicate a remarkable rigidity of the piecewise-polynomial ENO procedure.

Cited by in corpus (11)

• Construction of approximate entropy measure valued solutions for hyperbolic systems of conservation laws
• Local discrete velocity grids for deterministic rarefied flow simulations
• High-order accurate entropy stable finite difference schemes for the shallow water magnetohydrodynamics
• Entropy Symmetrization and High-Order Accurate Entropy Stable Numerical Schemes for Relativistic MHD Equations
• Formulation of Entropy-Stable schemes for the multicomponent compressible Euler equations
• High-order accurate entropy stable nodal discontinuous Galerkin schemes for the ideal special relativistic magnetohydrodynamics
• High-order finite-difference entropy stable schemes for two-fluid relativistic plasma flow equations
• Kinetic functions for nonclassical shocks, entropy stability, and discrete summation by parts
• Stability properties of the ENO method
• ENO-Based High-Order Data-Bounded and Constrained Positivity-Preserving Interpolation
• WENO interpolations and reconstructions using data bounded polynomial approximation