Summation-by-parts operators for general function spaces: the second derivative

Numerical approximation and computational geometry (primarily algorithms) (65Dxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Hyperbolic equations and hyperbolic systems (35Lxx)

Cites Work

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High order finite difference methods for the wave equation with non-conforming grid interfaces
Summation-by-parts in time
Review of summation-by-parts schemes for initial-boundary-value problems
A generalized framework for nodal first derivative summation-by-parts operators
A hybrid method for unsteady inviscid fluid flow
Summation by parts operators for finite difference approximations of second-derivatives with variable coefficients
Boundary closures for fourth-order energy stable weighted essentially non-oscillatory finite-difference schemes
Exponentially fitted spline in compression for the numerical solution of singular perturbation problems
Stable boundary treatment for the wave equation on second-order form
Revisiting and extending interface penalties for multi-domain summation-by-parts operators
Interface procedures for finite difference approximations of the advection-diffusion equation
Stable and accurate artificial dissipation
A short note on the error estimates of Yuan-Shu discontinuous Galerkin method based on non-polynomial approximation spaces
Discontinuous Galerkin method based on non-polynomial approximation spaces
High order finite difference methods for wave propagation in discontinuous media
A stable high-order finite difference scheme for the compressible Navier-Stokes equations: No-slip wall boundary conditions
Stable and accurate wave-propagation in discontinuous media
A systematic methodology for constructing high-order energy stable WENO schemes
A discontinuous \(hp\) finite element method for convection-diffusion problems
Summation by parts for finite difference approximations for \(d/dx\)
High order finite difference approximations of electromagnetic wave propagation close to material discontinuities
Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations
Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws
Stability of artificial dissipation and modal filtering for flux reconstruction schemes using summation-by-parts operators
Finite volume methods, unstructured meshes and strict stability for hyperbolic problems
Summation by parts operators for finite difference approximations of second derivatives
On the structure of function spaces in optimal recovery of point functionals for ENO-schemes by radial basis functions
A new class of \(A\) stable summation by parts time integration schemes with strong initial conditions
Stabilizing radial basis function methods for conservation laws using weakly enforced boundary conditions
On an eigenvalue property of summation-by-parts operators
Properties of Runge-Kutta-summation-by-parts methods
Stable high-order cubature formulas for experimental data
An energy-based summation-by-parts finite difference method for the wave equation in second order form
Some notes on summation by parts time integration methods
Analysis of the SBP-SAT stabilization for finite element methods. I: Linear problems
On the convergence rates of energy-stable finite-difference schemes
Stable high-order quadrature rules with equidistant points
Stable and accurate filtering procedures
Summation-by-parts operators for correction procedure via reconstruction
Discretely conservative finite-difference formulations for nonlinear conservation laws in split form: theory and boundary conditions
A stable and efficient hybrid scheme for viscous problems in complex geometries
Stable and accurate schemes for the compressible Navier-Stokes equations
A stable hybrid method for hyperbolic problems
Towards stable radial basis function methods for linear advection problems
Discrete vector calculus and Helmholtz Hodge decomposition for classical finite difference summation by parts operators
Summation-By-Parts in Time: The Second Derivative
A Skew-Symmetric Discontinuous Galerkin Spectral Element Discretization and Its Relation to SBP-SAT Finite Difference Methods
A Nonlinear Optimization Procedure for Generalized Gaussian Quadratures
A Comparison of the Dispersion and Dissipation Errors of Gauss and Gauss–Lobatto Discontinuous Galerkin Spectral Element Methods
Generalized Summation-by-Parts Operators for the Second Derivative
A Primer on Radial Basis Functions with Applications to the Geosciences
Total-Variation-Diminishing Time Discretizations
Generalized Gaussian Quadrature Rules for Systems of Arbitrary Functions
Shock capturing and high-order methods for hyperbolic conservation laws
A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations
Entropy stable essentially nonoscillatory methods based on RBF reconstruction
Solving Laplace Problems with Corner Singularities via Rational Functions
Solving PDEs with radial basis functions
Stability of correction procedure via reconstruction with summation-by-parts operators for Burgers' equation using a polynomial chaos approach
Multidimensional Summation-by-Parts Operators: General Theory and Application to Simplex Elements
The AAA Algorithm for Rational Approximation
On the Computation of Gaussian Quadrature Rules for Chebyshev Sets of Linearly Independent Functions
Summation-by-Parts Operators for General Function Spaces
Finite volume approximations and strict stability for hyperbolic problems
Multi-dimensional summation-by-parts operators for general function spaces: theory and construction
Analysis of the SBP-SAT stabilization for finite element methods. II: Entropy stability
Construction and application of provable positive and exact cubature formulas
Energy-stable global radial basis function methods on summation-by-parts form

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