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

ENO reconstruction and ENO interpolation are stable