Review of summation-by-parts schemes for initial-boundary-value problems
From MaRDI portal
Publication:349036
DOI10.1016/j.jcp.2014.02.031zbMath1349.65336arXiv1311.4984OpenAlexW1972670182MaRDI QIDQ349036
Publication date: 5 December 2016
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1311.4984
Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12)
Related Items
Simulations of plasmas and fluids using anti-symmetric models, Simultaneous approximation terms and functional accuracy for diffusion problems discretized with multidimensional summation-by-parts operators, An entropy-stable discontinuous Galerkin approximation of the Spalart-Allmaras turbulence model for the compressible Reynolds averaged Navier-Stokes equations, Nonlinear and linearised primal and dual initial boundary value problems: when are they bounded? How are they connected?, Reinterpretation and extension of entropy correction terms for residual distribution and discontinuous Galerkin schemes: application to structure preserving discretization, Energy stable wall modeling for the Navier-Stokes equations, Energy preserving turbulent simulations at a reduced computational cost, Uniformly best wavenumber approximations by spatial central difference operators, A new high order energy and enstrophy conserving Arakawa-like Jacobian differential operator, Nonlinearly stable flux reconstruction high-order methods in split form, Summation-by-parts operators for correction procedure via reconstruction, On Galerkin difference methods, A Legendre-Fourier spectral method with exact conservation laws for the Vlasov-Poisson system, Convergence of finite difference methods for the wave equation in two space dimensions, Generalized Summation-by-Parts Operators for the Second Derivative, Optimized explicit Runge-Kutta schemes for high-order collocated discontinuous Galerkin methods for compressible fluid dynamics, A new Eulerian model for viscous and heat conducting compressible flows, Positivity-preserving entropy stable schemes for the 1-D compressible Navier-Stokes equations: first-order approximation, Efficiency benchmarking of seventh-order tri-diagonal weighted compact nonlinear scheme on curvilinear mesh, Energy stable boundary conditions for the nonlinear incompressible Navier–Stokes equations, Weak versus strong wall boundary conditions for the incompressible Navier-Stokes equations, A unifying algebraic framework for discontinuous Galerkin and flux reconstruction methods based on the summation-by-parts property, Energy-based discontinuous Galerkin difference methods for second-order wave equations, Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes, Gradient preserved method for solving heat conduction equation with variable coefficients in double layers, Towards stable radial basis function methods for linear advection problems, Optimized geometrical metrics satisfying free-stream preservation, On the use of split forms and wall modeling to enable accurate high-Reynolds number discontinuous Galerkin simulations on body-fitted unstructured grids, Exact non-reflecting boundary conditions revisited: well-posedness and stability, On Port-Hamiltonian Approximation of a Nonlinear Flow Problem on Networks, Discrete vector calculus and Helmholtz Hodge decomposition for classical finite difference summation by parts operators, Entropy-stable multidimensional summation-by-parts discretizations on \textit{hp}-adaptive curvilinear grids for hyperbolic conservation laws, A new absorbing layer for simulation of wave propagation based on a KdV model on unbounded domain, Parallelization, initialization, and boundary treatments for the diamond scheme, Provably stable flux reconstruction high-order methods on curvilinear elements, A multi-domain summation-by-parts formulation for complex geometries, A stable and conservative nonlinear interface coupling for the incompressible Euler equations, Accurate high-order tensor-product generalized summation-by-parts discretizations of hyperbolic conservation laws: general curved domains and functional superconvergence, Coupling Requirements for Multiphysics Problems Posed on Two Domains, Entropy stable numerical approximations for the isothermal and polytropic Euler equations, An operator-based local discontinuous Galerkin method compatible with the BSSN formulation of the Einstein equations, A positivity preserving strategy for entropy stable discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations, Entropy-stable Gauss collocation methods for ideal magneto-hydrodynamics, Global and local conservation of mass, momentum and kinetic energy in the simulation of compressible flow, A new variational discretization technique for initial value problems bypassing governing equations, Higher-order accurate two-step finite difference schemes for the many-dimensional wave equation, Effective high-order energy stable flux reconstruction methods for first-order hyperbolic linear and nonlinear systems, Robust boundary conditions for stochastic incompletely parabolic systems of equations, On the order reduction of approximations of fractional derivatives: an explanation and a cure, A comparative study of two different shallow water formulations using stable summation by parts schemes, Parametric numerical study of passive scalar mixing in shock turbulence interaction, Excitation and resonance of acoustic-gravity waves in a column of stratified, bubbly magma, Some notes on summation by parts time integration methods, Data-driven discovery of PDEs in complex datasets, Encapsulated high order difference operators on curvilinear non-conforming grids, Entropy stable \(h/p\)-nonconforming discretization with the summation-by-parts property for the compressible Euler and Navier-Stokes equations, General relaxation methods for initial-value problems with application to multistep schemes, 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, Entropy stable artificial dissipation based on Brenner regularization of the Navier-Stokes equations, Structure-preserving algorithms for the two-dimensional sine-Gordon equation with Neumann boundary conditions, Multi-rate time integration on overset meshes, On the convergence rates of energy-stable finite-difference schemes, A general condition for kinetic-energy preserving discretization of flow transport equations, Entropy stable spectral collocation schemes for the 3-D Navier-Stokes equations on dynamic unstructured grids, The relation between primal and dual boundary conditions for hyperbolic systems of equations, On mass conservation and solvability of the discretized variable-density zero-Mach Navier-Stokes equations, Construction of modern robust nodal discontinuous Galerkin spectral element methods for the compressible Navier-Stokes equations, Inverses of SBP-SAT finite difference operators approximating the first and second derivative, On the order of Accuracy of Finite Difference Operators on Diagonal Norm Based Summation-by-Parts Form, Summation-by-Parts Operators for Non-Simply Connected Domains, Impact of wall modeling on kinetic energy stability for the compressible Navier-Stokes equations, Supraconservative Finite-Volume Methods for the Euler Equations of Subsonic Compressible Flow, A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations, Summation-by-Parts Approximations of the Second Derivative: Pseudoinverse and Revisitation of a High Order Accurate Operator, The Role of Numerical Boundary Procedures in the Stability of Perfectly Matched Layers, A Cartesian compact scheme for the Navier-Stokes equations in streamfunction formulation in irregular domains, Discontinuous Galerkin difference methods for symmetric hyperbolic systems, Accuracy of stable, high-order finite difference methods for hyperbolic systems with non-smooth wave speeds, Stable and accurate filtering procedures, Stable, high order accurate adaptive schemes for long time, highly intermittent geophysics problems, A Convergent Numerical Scheme for the Compressible Navier--Stokes Equations, Summation-By-Parts in Time: The Second Derivative, Superconvergent functional estimates from tensor-product generalized summation-by-parts discretizations in curvilinear coordinates, Entropy-stable, high-order summation-by-parts discretizations without interface penalties, Multigrid schemes for high order discretizations of hyperbolic problems, The Number of Boundary Conditions for Initial Boundary Value Problems, Energy Stability of Explicit Runge--Kutta Methods for Nonautonomous or Nonlinear Problems, The spatial operator in the incompressible Navier-Stokes, Oseen and Stokes equations, Fourier analysis and evaluation of DG, FD and compact difference methods for conservation laws, Boundary optimized diagonal-norm SBP operators, Stabilized seventh-order dissipative compact scheme using simultaneous approximation terms, Combining finite element and finite difference methods for isotropic elastic wave simulations in an energy-conserving manner, Well-Posedness, Stability and Conservation for a Discontinuous Interface Problem: An Initial Investigation, Generalized Summation by Parts Operators: Second Derivative and Time-Marching Methods, Unsteady Simulations of Rotor Stator Interactions Using SBP-SAT Schemes: Status and Challenges, Error boundedness of discontinuous Galerkin methods with variable coefficients, Extension of tensor-product generalized and dense-norm summation-by-parts operators to curvilinear coordinates, Dual time-stepping using second derivatives, On stochastic investigation of flow problems using the viscous Burgers' equation as an example, Summation-by-Parts Operators for General Function Spaces, Simulation of Wave Propagation Along Fluid-Filled Cracks Using High-Order Summation-by-Parts Operators and Implicit-Explicit Time Stepping, A stable FDTD subgridding scheme with SBP-SAT for transient TM analysis, Simulation of flexural-gravity wave propagation for elastic plates in shallow water using an energy-stable finite difference method with weakly enforced boundary and interface conditions, A discontinuous Galerkin discretization of elliptic problems with improved convergence properties using summation by parts operators, Multi-dimensional summation-by-parts operators for general function spaces: theory and construction, Boundary-optimized summation-by-parts operators for finite difference approximations of second derivatives with variable coefficients, Analysis of the SBP-SAT stabilization for finite element methods. II: Entropy stability, Analysis of an alternative Navier–Stokes system: Weak entropy solutions and a convergent numerical scheme, Adaptive energy stable artificial dissipation for preserving scalar boundedness in turbulent flows, Theoretical and practical aspects of space-time DG-SEM implementations, Convergence of Chandrashekar's second-derivative finite-volume approximation, A provably stable and high-order accurate finite difference approximation for the incompressible boundary layer equations, A superconvergent stencil-adaptive SBP-SAT finite difference scheme, Finite‐difference‐based simulation and adjoint optimization of gas networks, A symmetry and Noether charge preserving discretization of initial value problems, MultiLevel Local Time-Stepping Methods of Runge--Kutta-type for Wave Equations, On construction of shock-capturing boundary closures for high-order finite difference method, Mimetic finite differences for boundaries misaligned with grid nodes, Energy-stable global radial basis function methods on summation-by-parts form, Nonlinear boundary conditions for initial boundary value problems with applications in computational fluid dynamics, Order-Preserving Interpolation for Summation-by-Parts Operators at Nonconforming Grid Interfaces, Galerkin Differences for High-Order Partial Differential Equations, Spectral properties of the incompressible Navier-Stokes equations, Convergence of energy stable finite-difference schemes with interfaces, Practical inlet boundary conditions for internal flow calculations, Simultaneous-approximation-term based boundary discretization for moment equations of rarefied gas dynamics, Non-stiff boundary and interface penalties for narrow-stencil finite difference approximations of the Laplacian on curvilinear multiblock grids, Entropy-stable discontinuous Galerkin approximation with summation-by-parts property for the incompressible Navier-Stokes/Cahn-Hilliard system, An efficient finite difference method for the shallow water equations, Elastic wave propagation in anisotropic solids using energy-stable finite differences with weakly enforced boundary and interface conditions, High-order accurate entropy-stable discontinuous collocated Galerkin methods with the summation-by-parts property for compressible CFD frameworks: scalable SSDC algorithms and flow solver, A high-order finite-difference scheme to model the fluid-structure interaction in pneumatic seismic sources, Learning to differentiate, Neural network enhanced computations on coarse grids, Trace preserving quantum dynamics using a novel reparametrization-neutral summation-by-parts difference operator, A residual-based artificial viscosity finite difference method for scalar conservation laws, Properties of Runge-Kutta-summation-by-parts methods, On the robustness and performance of entropy stable collocated discontinuous Galerkin methods, Entropy stable boundary conditions for the Euler equations, On the role of global conservation property for finite difference schemes, An efficient hybrid method for uncertainty quantification, High-order finite difference method for the Schrödinger equation on deforming domains, Well-posedness, stability and conservation for a discontinuous interface problem, A stable domain decomposition technique for advection-diffusion problems, An improved high order finite difference method for non-conforming grid interfaces for the wave equation, High-fidelity sound propagation in a varying 3D atmosphere, Conservative and stable degree preserving SBP operators for non-conforming meshes, A dual consistent finite difference method with narrow stencil second derivative operators, \(L_2\) stability of explicit Runge-Kutta schemes, On pseudo-spectral time discretizations in summation-by-parts form, Generalised summation-by-parts operators and variable coefficients, A hybrid framework for coupling arbitrary summation-by-parts schemes on general meshes, Efficient fully discrete summation-by-parts schemes for unsteady flow problems, The effect of uncertain geometries on advection-diffusion of scalar quantities, Treatment of the polar coordinate singularity in axisymmetric wave propagation using high-order summation-by-parts operators on a staggered grid, High order finite difference methods for the wave equation with non-conforming grid interfaces, Insights on aliasing driven instabilities for advection equations with application to Gauss-Lobatto discontinuous Galerkin methods, Well-posed and stable transmission problems, A high-order compact difference algorithm for half-staggered grids for laminar and turbulent incompressible flows, Fully discrete energy stable high order finite difference methods for hyperbolic problems in deforming domains, An efficient time advancing strategy for energy-preserving simulations, A high order compact time/space finite difference scheme for the wave equation with variable speed of sound, High-order numerical methods for 2D parabolic problems in single and composite domains, Compatible diagonal-norm staggered and upwind SBP operators, A fully discrete, stable and conservative summation-by-parts formulation for deforming interfaces, Summation-by-parts operators with minimal dispersion error for coarse grid flow calculations, Extended skew-symmetric form for summation-by-parts operators and varying Jacobians, Corner-corrected diagonal-norm summation-by-parts operators for the first derivative with increased order of accuracy, Energy stable and high-order-accurate finite difference methods on staggered grids, On conservation and stability properties for summation-by-parts schemes, High-order asynchrony-tolerant finite difference schemes for partial differential equations, Entropy-stable summation-by-parts discretization of the Euler equations on general curved elements, Stable, non-dissipative, and conservative flux-reconstruction schemes in split forms, Convergence of summation-by-parts finite difference methods for the wave equation, A roadmap to well posed and stable problems in computational physics, On stable wall boundary conditions for the Hermite discretization of the linearised Boltzmann equation, Shallow water equations: split-form, entropy stable, well-balanced, and positivity preserving numerical methods, A new multigrid formulation for high order finite difference methods on summation-by-parts form, Using a characteristic-based particle tracking method to solve one-dimensional fully dynamic wave flow, A finite difference method for earthquake sequences in poroelastic solids, A stable dissipative compact finite difference scheme with global accuracy of ninth order, Stability of artificial dissipation and modal filtering for flux reconstruction schemes using summation-by-parts operators, Constructing non-reflecting boundary conditions using summation-by-parts in time, Simultaneous approximation terms for multi-dimensional summation-by-parts operators, Compact direct flux reconstruction for conservation laws, Stable dynamical adaptive mesh refinement, Mimetic properties of difference operators: product and chain rules as for functions of bounded variation and entropy stability of second derivatives, SBP-SAT finite difference discretization of acoustic wave equations on staggered block-wise uniform grids, A novel strategy for deriving high-order stable boundary closures based on global conservation. I: Basic formulas, An improved projection method, A general framework to construct schemes satisfying additional conservation relations. Application to entropy conservative and entropy dissipative schemes, Galerkin differences for acoustic and elastic wave equations in two space dimensions, Implicit boundary equations for conservative Navier-Stokes equations, Finite difference schemes with transferable interfaces for parabolic problems, Accurate gradient preserved method for solving heat conduction equations in double layers, An algorithmic exploration of the existence of high-order summation by parts operators with diagonal norm, A kinetic energy preserving DG scheme based on Gauss-Legendre points, Entropy-stable \(p\)-nonconforming discretizations with the summation-by-parts property for the compressible Navier-Stokes equations, 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, Kinetic functions for nonclassical shocks, entropy stability, and discrete summation by parts, On entropy-stable discretizations and the entropy adjoint, On long time error bounds for the wave equation on second order form, Hyperbolic systems of equations posed on erroneous curved domains, Assessment of variational multiscale models for the large eddy simulation of turbulent incompressible flows, A high order accurate finite difference method for the Drinfel'd-Sokolov-Wilson equation, Entropy conserving and kinetic energy preserving numerical methods for the Euler equations using summation-by-parts operators, On the rate of error growth in time for numerical solutions of nonlinear dispersive wave equations, Development and analysis of entropy stable no-slip wall boundary conditions for the Eulerian model for viscous and heat conducting compressible flows, High-order compact difference schemes on wide computational stencils with a spectral-like accuracy, Accurate solution-adaptive finite difference schemes for coarse and fine grids, Optimization of multidimensional diagonal-norm summation-by-parts operators on simplices, Eigenanalysis and non-modal analysis of collocated discontinuous Galerkin discretizations with the summation-by-parts property, Conservative finite difference time domain schemes for the prestressed Timoshenko, shear and Euler-Bernoulli beam equations, A dynamically load-balanced parallel \(p\)-adaptive implicit high-order flux reconstruction method for under-resolved turbulence simulation, Entropy stability for the compressible Navier-Stokes equations with strong imposition of the no-slip boundary condition, A skew-symmetric energy and entropy stable formulation of the compressible Euler equations, On an eigenvalue property of summation-by-parts operators, Implicit summation by parts operators for finite difference approximations of first and second derivatives, First-order positivity-preserving entropy stable scheme for the 3-D compressible Navier-Stokes equations, Extending EB3 scheme for the differential conservation law from node-centered to cell-centered control volumes. I: Basic formula on regular cells, Provably non-stiff implementation of weak coupling conditions for hyperbolic problems
Cites Work
- From Semidiscrete to Fully Discrete: Stability of Runge--Kutta Schemes by The Energy Method
- Entropy stability theory for difference approximations of nonlinear conservation laws and related time-dependent problems
- Summation by Parts, Projections, and Stability. I
- Summation by Parts, Projections, and Stability. II
- Stable and Accurate Second-order Formulation of the Shifted Wave Equation
- Fluid Structure Interaction Problems: the Necessity of a Well Posed, Stable and Accurate Formulation
- Scattering of an entropy disturbance into sound by a symmetric thin body
- High Order Difference Methods for Time Dependent PDE
- A multi-block infrastructure for three-dimensional time-dependent numerical relativity
- On error bounds of finite difference approximations to partial differential equations. -- Temporal behavior and rate of convergence
- Finite volume approximations and strict stability for hyperbolic problems
- High-order finite difference methods, multidimensional linear problems, and curvilinear coordinates
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Energy stable flux reconstruction schemes for advection-diffusion problems on triangles
- Summation-by-parts in time
- High-order entropy stable finite difference schemes for nonlinear conservation laws: finite domains
- High-order accurate difference schemes for the Hodgkin-Huxley equations
- Dual consistency and functional accuracy: a finite-difference perspective
- A stochastic Galerkin method for the Euler equations with roe variable transformation
- Duality based boundary conditions and dual consistent finite difference discretizations of the Navier-Stokes and Euler equations
- High order numerical simulation of aeolian tones
- Output error estimation for summation-by-parts finite-difference schemes
- Interaction of waves with frictional interfaces using summation-by-parts difference operators: weak enforcement of nonlinear boundary conditions
- A hybrid method for unsteady inviscid fluid flow
- Numerical simulation of confined pulsating jets in human phonation
- A computational study of vortex-airfoil interaction using high-order finite difference methods
- Weak and strong wall boundary procedures and convergence to steady-state of the Navier-Stokes equations
- Spectral analysis of the continuous and discretized heat and advection equation on single and multiple domains
- Third-order accurate entropy-stable schemes for initial-boundary-value conservation laws
- Summation-by-parts operators and high-order quadrature
- On the linear stability of the fifth-order WENO discretization
- Boundary closures for fourth-order energy stable weighted essentially non-oscillatory finite-difference schemes
- Boundary procedures for the time-dependent Burgers' equation under uncertainty
- A stable and conservative method for locally adapting the design order of finite difference schemes
- Implicit-explicit schemes for flow equations with stiff source terms
- Fourth-order Runge-Kutta schemes for fluid mechanics applications
- Stable boundary treatment for the wave equation on second-order form
- Accuracy of the simultaneous-approximation-term boundary condition for time-dependent problems
- Revisiting and extending interface penalties for multi-domain summation-by-parts operators
- Interface procedures for finite difference approximations of the advection-diffusion equation
- Stable Robin solid wall boundary conditions for the Navier-Stokes equations
- Designing an efficient solution strategy for fluid flows. I: A stable high order finite difference scheme and sharp shock resolution for the Euler equations
- Implicit time integration schemes for the unsteady compressible Navier-Stokes equations: Laminar flow
- Stable and accurate artificial dissipation
- Stable artificial dissipation operators for finite volume schemes on unstructured grids
- On the order of accuracy for difference approximations of initial-boundary value problems
- High order finite difference methods for wave propagation in discontinuous media
- Conservative finite difference formulations, variable coefficients, energy estimates and artificial dissipation
- A stable high-order finite difference scheme for the compressible Navier-Stokes equations: No-slip wall boundary conditions
- A stable and high-order accurate conjugate heat transfer problem
- An adaptive implicit-explicit scheme for the DNS and LES of compressible flows on unstructured grids
- Third-order energy stable WENO scheme
- A stable and conservative high order multi-block method for the compressible Navier-Stokes equations
- Numerical analysis of the Burgers' equation in the presence of uncertainty
- High-order accurate computations for unsteady aerodynamics
- Boundary conditions for nonlinear hyperbolic systems of conservation laws
- Optimal time splitting for two- and three-dimensional Navier-Stokes equations with mixed derivatives
- A diagonal form of an implicit approximate-factorization algorithm
- A stable and conservative interface treatment of arbitrary spatial accuracy
- Boundary and interface conditions for high-order finite-difference methods applied to the Euler and Navier-Stokes equations
- Designing an efficient solution strategy for fluid flows. II: Stable high-order central finite difference schemes on composite adaptive grids with sharp shock resolution
- Summation by parts for finite difference approximations for \(d/dx\)
- Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes
- Asymptotically stable fourth-order accurate schemes for the diffusion equation on complex shapes
- Boundary procedures for summation-by-parts operators
- High order finite difference approximations of electromagnetic wave propagation close to material discontinuities
- On coordinate transformations for summation-by-parts operators
- Low-storage, explicit Runge-Kutta schemes for the compressible Navier-Stokes equations
- Entropy splitting for high-order numerical simulation of vortex sound at low Mach numbers
- On the stability definition of difference approximations for the initial boundary value problem
- Finite volume methods, unstructured meshes and strict stability for hyperbolic problems
- Additive Runge-Kutta schemes for convection-diffusion-reaction equations
- Stability of finite volume approximations for the Laplacian operator on quadrilateral and triangular grids
- Summation by parts operators for finite difference approximations of second derivatives
- The use of characteristic boundary conditions for the Navier-Stokes equations
- Efficient implementation of weighted ENO schemes
- Entropy stable schemes for initial-boundary-value conservation laws
- Stability at nonconforming grid interfaces for a high order discretization of the Schrödinger equation
- Multi-dimensional asymptotically stable finite difference schemes for the advection-diffusion equation
- Strict stability of high-order compact implicit finite-difference schemes: The role of boundary conditions for hyperbolic PDEs. I
- Strict stability of high-order compact implicit finite-difference schemes: The role of boundary conditions for hyperbolic PDEs. II
- An intrusive hybrid method for discontinuous two-phase flow under uncertainty
- Conjugate heat transfer for the unsteady compressible Navier-Stokes equations using a multi-block coupling
- On stability of numerical schemes via frozen coefficients and the magnetic induction equations
- Boundary conditions for a divergence-free velocity-pressure formulation of the Navier-Stokes equations
- A stable high-order finite difference scheme for the compressible Navier-Stokes equations, far-field boundary conditions
- Higher order finite difference schemes for the magnetic induction equations
- Simulation of dynamic earthquake ruptures in complex geometries using high-order finite difference methods
- Entropy-stable schemes for the Euler equations with far-field and wall boundary conditions
- Superconvergent functional output for time-dependent problems using finite differences on summation-by-parts form
- Discretely conservative finite-difference formulations for nonlinear conservation laws in split form: theory and boundary conditions
- On the impact of boundary conditions on dual consistent finite difference discretizations
- On stability and monotonicity requirements of finite difference approximations of stochastic conservation laws with random viscosity
- A stable and efficient hybrid scheme for viscous problems in complex geometries
- Stable and accurate schemes for the compressible Navier-Stokes equations
- Accurate partial difference methods. II: Non-linear problems
- Steady-state computations using summation-by-parts operators
- A stable hybrid method for hyperbolic problems
- Optimized high-order derivative and dissipation operators satisfying summation by parts, and applications in three-dimensional multi-block evolutions
- A Skew-Symmetric Discontinuous Galerkin Spectral Element Discretization and Its Relation to SBP-SAT Finite Difference Methods
- Higher-order finite difference schemes for the magnetic induction equations with resistivity
- Towards Time-Stable and Accurate LES on Unstructured Grids
- Stable and Accurate Interpolation Operators for High-Order Multiblock Finite Difference Methods
- Superconvergent Functional Estimates from Summation-By-Parts Finite-Difference Discretizations
- Survey of the stability of linear finite difference equations
- Symmetrizable Finite Difference Operators
- Linear Instability of the Fifth-Order WENO Method
- Error Bounded Schemes for Time-dependent Hyperbolic Problems
- Stability Theory of Difference Approximations for Multidimensional Initial-Boundary Value Problems
- Convergence Theorem for Difference Approximations of Hyperbolic Quasi- Initial-Boundary Value Problems
- An Extension of the Kreiss Matrix Theorem
- The Convergence Rate for Difference Approximations to General Mixed Initial-Boundary Value Problems
- The Convergence Rate for Difference Approximations to Mixed Initial Boundary Value Problems