Summation by parts for finite difference approximations for d/dx
Journal of Computational Physics
A Stable Penalty Method for the Compressible Navier--Stokes Equations: I. Open Boundary Conditions
SIAM Journal on Scientific Computing
Spectral methods on arbitrary grids
Journal of Computational Physics
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
A stable and conservative interface treatment of arbitrary spatial accuracy
Journal of Computational Physics
Journal of Computational Physics
Finite volume approximations and strict stability for hyperbolic problems
Applied Numerical Mathematics
Boundary Procedures for Summation-by-Parts Operators
Journal of Scientific Computing
Finite volume methods, unstructured meshes and strict stability for hyperbolic problems
Applied Numerical Mathematics
On Coordinate Transformations for Summation-by-Parts Operators
Journal of Scientific Computing
Stable and Accurate Artificial Dissipation
Journal of Scientific Computing
Applied Numerical Mathematics
Summation by parts operators for finite difference approximations of second derivatives
Journal of Computational Physics
Journal of Computational Physics
Barycentric rational interpolation with no poles and high rates of approximation
Numerische Mathematik
Stable and accurate schemes for the compressible Navier-Stokes equations
Journal of Computational Physics
Is Gauss Quadrature Better than Clenshaw-Curtis?
SIAM Review
Numerical Methods for Special Functions
Numerical Methods for Special Functions
A stable high-order finite difference scheme for the compressible Navier-Stokes equations
Journal of Computational Physics
Third-order Energy Stable WENO scheme
Journal of Computational Physics
A systematic methodology for constructing high-order energy stable WENO schemes
Journal of Computational Physics
A stable and conservative high order multi-block method for the compressible Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
Convergence rates of derivatives of a family of barycentric rational interpolants
Applied Numerical Mathematics
Interface procedures for finite difference approximations of the advection-diffusion equation
Journal of Computational and Applied Mathematics
Superconvergent Functional Estimates from Summation-By-Parts Finite-Difference Discretizations
SIAM Journal on Scientific Computing
Journal of Computational Physics
Journal of Scientific Computing
Summation-by-parts operators and high-order quadrature
Journal of Computational and Applied Mathematics
Dual consistency and functional accuracy: a finite-difference perspective
Journal of Computational Physics
Hi-index | 31.45 |
A generalized framework is presented that extends the classical theory of finite-difference summation-by-parts (SBP) operators to include a wide range of operators, where the main extensions are (i) non-repeating interior point operators, (ii) nonuniform nodal distribution in the computational domain, (iii) operators that do not include one or both boundary nodes. Necessary and sufficient conditions are proven for the existence of nodal approximations to the first derivative with the SBP property. It is proven that the positive-definite norm matrix of each SBP operator must be associated with a quadrature rule; moreover, given a quadrature rule there exists a corresponding SBP operator, where for diagonal-norm SBP operators the weights of the quadrature rule must be positive. The generalized framework gives a straightforward means of posing many known approximations to the first derivative as SBP operators; several are surveyed, such as discontinuous Galerkin discretizations based on the Legendre-Gauss quadrature points, and shown to be SBP operators. Moreover, the new framework provides a method for constructing SBP operators by starting from quadrature rules; this is illustrated by constructing novel SBP operators from known quadrature rules. To demonstrate the utility of the generalization, the Legendre-Gauss and Legendre-Gauss-Radau quadrature points are used to construct SBP operators that do not include one or both boundary nodes.