Summation-by-Parts Operators for General Function Spaces
From MaRDI portal
Publication:5889027
DOI10.1137/22M1470141MaRDI QIDQ5889027
Jan Glaubitz, Jan Nordström, Philipp Öffner
Publication date: 26 April 2023
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2203.05479
trigonometric functionsradial basis functionsexponential functionssummation-by-parts operatorsmimetic discretizationgeneral function spaces
Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Numerical methods for trigonometric approximation and interpolation (65T40) Numerical differentiation (65D25) Numerical radial basis function approximation (65D12)
Related Items (4)
Multi-dimensional summation-by-parts operators for general function spaces: theory and construction ⋮ A symmetry and Noether charge preserving discretization of initial value problems ⋮ A new variable shape parameter strategy for RBF approximation using neural networks ⋮ Energy-stable global radial basis function methods on summation-by-parts form
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Summation-by-parts in time
- High-order entropy stable finite difference schemes for nonlinear conservation laws: finite domains
- Review of summation-by-parts schemes for initial-boundary-value problems
- A generalized framework for nodal first derivative summation-by-parts operators
- Summation-by-parts operators and high-order quadrature
- 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 and accurate artificial dissipation
- A short note on the error estimates of Yuan-Shu discontinuous Galerkin method based on non-polynomial approximation spaces
- Diagonal-norm summation by parts operators for finite difference approximations of third and fourth derivatives
- Discontinuous Galerkin method based on non-polynomial approximation spaces
- Conservative finite difference formulations, variable coefficients, energy estimates and artificial dissipation
- A systematic methodology for constructing high-order energy stable WENO schemes
- Summation by parts for finite difference approximations for \(d/dx\)
- Gaussian quadrature for products of exponential functions
- A stable domain decomposition technique for advection-diffusion problems
- Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations
- Diagonal-norm upwind SBP operators
- Energy stable and high-order-accurate finite difference methods on staggered grids
- Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws
- On conservation and stability properties for summation-by-parts schemes
- 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
- Stable high-order randomized cubature formulae in arbitrary dimension
- Properties of Runge-Kutta-summation-by-parts methods
- Stable high-order cubature formulas for experimental data
- Reinterpretation and extension of entropy correction terms for residual distribution and discontinuous Galerkin schemes: application to structure preserving discretization
- Encapsulated high order difference operators on curvilinear non-conforming grids
- Analysis of the SBP-SAT stabilization for finite element methods. I: Linear problems
- Staggered-grid entropy-stable multidimensional summation-by-parts discretizations on curvilinear coordinates
- RBF moment computation and meshless cubature on general polygonal regions
- Stable high-order quadrature rules with equidistant points
- Stable discretisations of high-order discontinuous Galerkin methods on equidistant and scattered points
- Error boundedness of discontinuous Galerkin methods with variable coefficients
- Summation-by-parts operators for correction procedure via reconstruction
- Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations
- Discretely conservative finite-difference formulations for nonlinear conservation laws in split form: theory and boundary conditions
- Towards stable radial basis function methods for linear advection problems
- Towards stability results for global radial basis function based quadrature formulas
- A Skew-Symmetric Discontinuous Galerkin Spectral Element Discretization and Its Relation to SBP-SAT Finite Difference Methods
- Entropy Stable Spectral Collocation Schemes for the Navier--Stokes Equations: Discontinuous Interfaces
- Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments
- A Comparison of the Dispersion and Dissipation Errors of Gauss and Gauss–Lobatto Discontinuous Galerkin Spectral Element Methods
- A Primer on Radial Basis Functions with Applications to the Geosciences
- A higher-order discontinuous enrichment method for the solution of high péclet advection-diffusion problems on unstructured meshes
- The Numerical Viscosity of Entropy Stable Schemes for Systems of Conservation Laws. I
- Total-Variation-Diminishing Time Discretizations
- TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
- Energy stable boundary conditions for the nonlinear incompressible Navier–Stokes equations
- On the order of Accuracy of Finite Difference Operators on Diagonal Norm Based Summation-by-Parts Form
- Shock capturing and high-order methods for hyperbolic conservation laws
- Stable High Order Quadrature Rules for Scattered Data and General Weight Functions
- 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
- Scattered Data Approximation
- Finite volume approximations and strict stability for hyperbolic problems
- Construction and application of provable positive and exact cubature formulas
This page was built for publication: Summation-by-Parts Operators for General Function Spaces
