The stability of numerical boundary treatments for compact high-order finite-difference schemes
Journal of Computational Physics
Summation by parts for finite difference approximations for d/dx
Journal of Computational Physics
Fourth-order difference methods for hyperbolic IBVPs
Journal of Computational Physics
Summation by parts, projections, and stability. I
Mathematics of Computation
Summation by parts, projections, and stability. II
Mathematics of Computation
Designing an efficient solution strategy for fluid flows
Journal of Computational Physics
Asymptotically stable fourth-order accurate schemes for the diffusion equation on complex shapes
Journal of Computational Physics
A stable and conservative interface treatment of arbitrary spatial accuracy
Journal of Computational Physics
Low-dissipative high-order shock-capturing methods using characteristic-based filters
Journal of Computational Physics
Boundary Procedures for Summation-by-Parts Operators
Journal of Scientific Computing
Bounded Error Schemes for the Wave Equation on Complex Domains
Bounded Error Schemes for the Wave Equation on Complex Domains
Multiresolution Wavelet Based Adaptive Numerical Dissipation Control for Shock-Turbulence Computations
Stable and Accurate Artificial Dissipation
Journal of Scientific Computing
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
High-Order Compact ADI Methods for Parabolic Equations
Computers & Mathematics with Applications
Journal of Computational Physics
Journal of Computational Physics
A stable and efficient hybrid scheme for viscous problems in complex geometries
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
A methodology for the development of discrete adjoint solvers using automatic differentiation tools
International Journal of Computational Fluid Dynamics
Stable and accurate wave-propagation in discontinuous media
Journal of Computational Physics
A high-order super-grid-scale absorbing layer and its application to linear hyperbolic systems
Journal of Computational Physics
Analysis of the order of accuracy for node-centered finite volume schemes
Applied Numerical Mathematics
Stable Boundary Treatment for the Wave Equation on Second-Order Form
Journal of Scientific Computing
Revisiting and Extending Interface Penalties for Multi-domain Summation-by-Parts Operators
Journal of Scientific Computing
SIAM Journal on Scientific Computing
Stable and Accurate Interpolation Operators for High-Order Multiblock Finite Difference Methods
SIAM Journal on Scientific Computing
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
Output error estimation for summation-by-parts finite-difference schemes
Journal of Computational Physics
Journal of Computational Physics
Shock structure in numerical solutions of the Navier-Stokes and Bhatnagar-Gross-Krook equations
Mathematical and Computer Modelling: An International Journal
Journal of Computational Physics
Journal of Scientific Computing
Journal of Scientific Computing
Applied Numerical Mathematics
Grid stabilization of high-order one-sided differencing II: Second-order wave equations
Journal of Computational Physics
Journal of Computational Physics
Journal of Scientific Computing
High Order Stable Finite Difference Methods for the Schrödinger Equation
Journal of Scientific Computing
Journal of Scientific Computing
High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains
Journal of Computational Physics
High-order accurate difference schemes for the Hodgkin-Huxley equations
Journal of Computational Physics
Journal of Computational Physics
Computers & Mathematics with Applications
Dual consistency and functional accuracy: a finite-difference perspective
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Mimetic finite difference method
Journal of Computational Physics
Journal of Computational Physics
High-fidelity numerical solution of the time-dependent Dirac equation
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
Hi-index | 31.58 |
Finite difference operators approximating second derivatives and satisfying a summation by parts rule have been derived for the fourth, sixth and eighth order case by using the symbolic mathematics software Maple. The operators are based on the same norms as the corresponding approximations of the first derivative, which makes the construction of stable approximations to general parabolic problems straightforward. The error analysis shows that the second derivative approximation can be closed at the boundaries with an approximation two orders less accurate than the internal scheme, and still preserve the internal accuracy.