Correction: High-Order Artificial Dissipation Operators Possessing the Summation-By-Parts Property

The summation-by-parts (SBP) property can be used to construct high-order provably stable numerical methods. A general framework is explored for deriving provably stable and conservative artificial dissipation operators for use with high-order traditional and elementtype SBP operators on general nodal distributions, thus enabling the time stable and accurate solution of practical nonlinear problems, including those problems that contain variable coe cients, for example, aerodynamics problems involving the compressible Euler and NavierStokes equations. The basic premise is presented for scalar conservation laws and then extended to entropy stability for systems. Artificial dissipation operators for use with traditional SBP operators are constructed having 1st, 3rd, 5th, and 7th order accuracy on the interior achieved with minimum-width stencils that have ample flexibility in the derivation of novel accuracy-preserving boundary closures. Element-type dissipation operators are constructed on the Legendre-Gauss and Legendre-Gauss-Lobatto nodal distributions. The stability and accuracy properties of a suite of the constructed artificial dissipation operators are characterized in the numerical solution of the quasi-one-dimensional Euler equations applied to a converging-diverging nozzle.