Stability properties of the ENO method
For researchers in numerical methods for conservation laws, this review consolidates known stability results and their implications for high-order scheme convergence.
The paper reviews stability properties of the ENO reconstruction method, including monotonicity, non-oscillatory behavior, and total variation-type bounds, and outlines their application to derive stability and convergence of high-order schemes for conservation laws.
We review the currently available stability properties of the ENO reconstruction procedure, such as its monotonicity and non-oscillatory properties, the sign property, upper bounds on cell interface jumps and a total variation-type bound. We also outline how these properties can be applied to derive stability and convergence of high-order accurate schemes for conservation laws.