Summation by parts for finite difference approximations for d/dx

On Error Bounds of Finite Difference Approximations to Partial Differential Equations—Temporal Behavior and Rate of Convergence

Journal of Scientific Computing

High-order time-stable numerical boundary scheme for the temporally dependent Maxwell equations in two dimensions

Journal of Computational Physics

Entropy splitting for high-order numerical simulation of compressible turbulence

Journal of Computational Physics

Entropy Splitting for High Order Numerical Simulation of Vortex Sound at Low Mach Numbers

Journal of Scientific Computing

High Order Finite Difference Approximations of Electromagnetic Wave Propagation Close to Material Discontinuities

Journal of Scientific Computing

Grid convergence of high order methods for multiscale complex unsteady viscous compressible flows

Journal of Computational Physics

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

High-order non-uniform grid schemes for numerical simulation of hypersonic boundary-layer stability and transition

Journal of Computational Physics

Stable and Accurate Artificial Dissipation

Journal of Scientific Computing

Summation by parts operators for finite difference approximations of second derivatives

Journal of Computational Physics

Higher entropy conservation and numerical stability of compressible turbulence simulations

Journal of Computational Physics

A stable hybrid method for hyperbolic problems

Journal of Computational Physics

Short note: A high-order Padé ADI method for unsteady convection-diffusion equations

Journal of Computational Physics

On the order of accuracy for difference approximations of initial-boundary value problems

Journal of Computational Physics

High order finite difference methods for wave propagation in discontinuous media

Journal of Computational Physics

A low numerical dissipation patch-based adaptive mesh refinement method for large-eddy simulation of compressible flows

Journal of Computational Physics

Grid stabilization of high-order one-sided differencing I: First-order hyperbolic systems

Journal of Computational Physics

Optimized High-Order Derivative and Dissipation Operators Satisfying Summation by Parts, and Applications in Three-dimensional Multi-block Evolutions

Journal of Scientific Computing

Boundary conditions for a divergence free velocity-pressure formulation of the Navier-Stokes equations

Journal of Computational Physics

A stable high-order finite difference scheme for the compressible Navier-Stokes equations, far-field boundary conditions

Journal of Computational Physics

A stable and efficient hybrid scheme for viscous problems in complex geometries

Journal of Computational Physics

A class of energy stable, high-order finite-difference interface schemes suitable for adaptive mesh refinement of hyperbolic problems

Journal of Computational Physics

Stable and accurate schemes for the compressible Navier-Stokes equations

Journal of Computational Physics

A stable high-order finite difference scheme for the compressible Navier-Stokes equations

Journal of Computational Physics

Verification of a fluid-dynamics solver using correlations with linear stability results

Journal of Computational Physics

Stable and accurate wave-propagation in discontinuous media

Journal of Computational Physics

Symmetry-preserving upwind discretization of convection on non-uniform grids

Applied Numerical Mathematics

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

Nondissipative and energy-stable high-order finite-difference interface schemes for 2-D patch-refined grids

Journal of Computational Physics

Numerical analysis of the Burgers' equation in the presence of uncertainty

Journal of Computational Physics

A stable and conservative high order multi-block method for the compressible Navier-Stokes equations

Journal of Computational Physics

Stable Boundary Treatment for the Wave Equation on Second-Order Form

Journal of Scientific Computing

A low numerical dissipation immersed interface method for the compressible Navier-Stokes equations

Journal of Computational Physics

A stable and high-order accurate conjugate heat transfer problem

Journal of Computational Physics

Revisiting and Extending Interface Penalties for Multi-domain Summation-by-Parts Operators

Journal of Scientific Computing

Stabilized non-dissipative approximations of Euler equations in generalized curvilinear coordinates

Journal of Computational Physics

Stable and Accurate Interpolation Operators for High-Order Multiblock Finite Difference Methods

SIAM Journal on Scientific Computing

Boundary closures for fourth-order energy stable weighted essentially non-oscillatory finite-difference schemes

Journal of Computational Physics

Stable Robin solid wall boundary conditions for the Navier-Stokes equations

Journal of Computational Physics

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

Derivation of Strictly Stable High Order Difference Approximations for Variable-Coefficient PDE

Journal of Scientific Computing

Interaction of Waves with Frictional Interfaces Using Summation-by-Parts Difference Operators: Weak Enforcement of Nonlinear Boundary Conditions

Journal of Scientific Computing

Output error estimation for summation-by-parts finite-difference schemes

Journal of Computational Physics

Weak and strong wall boundary procedures and convergence to steady-state of the Navier-Stokes equations

Journal of Computational Physics

Mass, momentum and energy conserving (MaMEC) discretizations on general grids for the compressible Euler and shallow water equations

Journal of Computational Physics

Energy stable numerical methods for hyperbolic partial differential equations using overlapping domain decomposition

Journal of Computational Physics

High Order Finite Difference and Finite Volume Methods for Advection on the Sphere

Journal of Scientific Computing

A Fourth Order Accurate Finite Difference Scheme for the Elastic Wave Equation in Second Order Formulation

Journal of Scientific Computing

Spectral analysis of the continuous and discretized heat and advection equation on single and multiple domains

Applied Numerical Mathematics

Summation-by-parts operators and high-order quadrature

Journal of Computational and Applied Mathematics

Grid stabilization of high-order one-sided differencing II: Second-order wave equations

Journal of Computational Physics

On the impact of boundary conditions on dual consistent finite difference discretizations

Journal of Computational Physics

High Order Stable Finite Difference Methods for the Schrödinger Equation

Journal of Scientific Computing

Simulation of Dynamic Earthquake Ruptures in Complex Geometries Using High-Order Finite Difference Methods

Journal of Scientific Computing

Summation-by-parts in time

Journal of Computational Physics

Boundary treatment for fourth-order staggered mesh discretizations of the incompressible Navier-Stokes equations

Journal of Computational Physics

Duality based boundary conditions and dual consistent finite difference discretizations of the Navier-Stokes and Euler equations

Journal of Computational Physics

A Cartesian-based embedded geometry technique with adaptive high-order finite differences for compressible flow around complex geometries

Journal of Computational Physics

Optimal diagonal-norm SBP operators

Journal of Computational Physics

A generalized framework for nodal first derivative summation-by-parts operators

Journal of Computational Physics