ENO reconstruction and ENO interpolation are stable
Provides theoretical stability guarantees for ENO schemes, which are widely used in numerical PDEs, but the results are incremental as they confirm expected behavior.
The paper proves stability estimates for ENO reconstruction and interpolation, showing sign preservation and boundedness of jumps across cell interfaces for arbitrary order on non-uniform meshes.
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.