Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations
type: Item
instance of: scholarly article
title: Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations
zbMATH Open document ID: 1390.65064
author: David C. Del Rey Fernández
author: D. W. Zingg
author: J. E. Hicken
published in: Computers and Fluids
publication date: 2018-06-19T00:00:00Z
Mathematics Subject Classification ID: 65M06
zbMATH DE Number: 6891165
zbMATH Keywords: summation-by-parts operators
zbMATH Keywords: finite-difference methods
zbMATH Keywords: simultaneous approximation terms
zbMATH Keywords: boundary closures
zbMATH Keywords: numerical boundary schemes
zbMATH Keywords: higher-order methods
zbMATH Keywords: stability
zbMATH Keywords: energy-method
MaRDI profile type: Publication
full work available at URL: j.compfluid.2014.02.016
OpenAlex ID: W2065978762
cites work: The Relative Efficiency of Finite Difference and Finite Element Methods. I: Hyperbolic Problems and Splines
cites work: High-order Finite Difference and Finite Volume WENO Schemes and Discontinuous Galerkin Methods for CFD
cites work: Numerical solution of the time-domain Maxwell equations using high-accuracy finite-difference methods
cites work: Q4127319
cites work: The Convergence Rate for Difference Approximations to Mixed Initial Boundary Value Problems
cites work: Summation by parts for finite difference approximations for \(d/dx\)
cites work: Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes
cites work: Domain decomposition methods for pseudo spectral approximations. I. Second order equations in one dimension
cites work: A New Method of Imposing Boundary Conditions in Pseudospectral Approximations of Hyperbolic Equations
cites work: Summation by Parts, Projections, and Stability. I
cites work: Summation by Parts, Projections, and Stability. II
cites work: A stable and conservative interface treatment of arbitrary spatial accuracy
cites work: Boundary and interface conditions for high-order finite-difference methods applied to the Euler and Navier-Stokes equations
cites work: High-order finite difference methods, multidimensional linear problems, and curvilinear coordinates
cites work: Boundary procedures for summation-by-parts operators
cites work: A stable high-order finite difference scheme for the compressible Navier-Stokes equations, far-field boundary conditions
cites work: A stable high-order finite difference scheme for the compressible Navier-Stokes equations: No-slip wall boundary conditions
cites work: A stable and conservative high order multi-block method for the compressible Navier-Stokes equations
cites work: Stable Robin solid wall boundary conditions for the Navier-Stokes equations
cites work: Optimized high-order derivative and dissipation operators satisfying summation by parts, and applications in three-dimensional multi-block evolutions
cites work: Summation by parts operators for finite difference approximations of second derivatives
cites work: On the order of accuracy for difference approximations of initial-boundary value problems
cites work: Stable and accurate schemes for the compressible Navier-Stokes equations
cites work: High-Order Narrow Stencil Finite-Difference Approximations of Second-Order Derivatives Involving Variable Coefficients
cites work: Summation by parts operators for finite difference approximations of second-derivatives with variable coefficients
cites work: Stable and accurate artificial dissipation
cites work: Conservative finite difference formulations, variable coefficients, energy estimates and artificial dissipation
cites work: Entropy splitting for high-order numerical simulation of compressible turbulence
cites work: Entropy splitting and numerical dissipation
cites work: Q5702451
cites work: Discretely conservative finite-difference formulations for nonlinear conservation laws in split form: theory and boundary conditions
cites work: High-order entropy stable finite difference schemes for nonlinear conservation laws: finite domains
cites work: On coordinate transformations for summation-by-parts operators
cites work: Superconvergent Functional Estimates from Summation-By-Parts Finite-Difference Discretizations
cites work: Dual consistency and functional accuracy: a finite-difference perspective
cites work: Summation-by-parts operators and high-order quadrature
cites work: Superconvergent functional output for time-dependent problems using finite differences on summation-by-parts form
cites work: Revisiting and extending interface penalties for multi-domain summation-by-parts operators
cites work: High-order accurate computations for unsteady aerodynamics
cites work: A computational study of vortex-airfoil interaction using high-order finite difference methods
cites work: Grid convergence of high order methods for multiscale complex unsteady viscous compressible flows.
cites work: A stable and high-order accurate conjugate heat transfer problem
cites work: Conjugate heat transfer for the unsteady compressible Navier-Stokes equations using a multi-block coupling
cites work: Numerical analysis of the Burgers' equation in the presence of uncertainty
cites work: Boundary procedures for the time-dependent Burgers' equation under uncertainty
cites work: On stability and monotonicity requirements of finite difference approximations of stochastic conservation laws with random viscosity
cites work: Higher order finite difference schemes for the magnetic induction equations
cites work: On stability of numerical schemes via frozen coefficients and the magnetic induction equations
cites work: Higher-order finite difference schemes for the magnetic induction equations with resistivity
cites work: High order finite difference approximations of electromagnetic wave propagation close to material discontinuities
cites work: Stable and accurate wave-propagation in discontinuous media
cites work: Stable boundary treatment for the wave equation on second-order form
cites work: Numerical investigation and modelling of acoustically excited flow through a circular orifice backed by a hexagonal cavity
cites work: High Order Difference Methods for Time Dependent PDE
cites work: Time dependent problems and difference methods
cites work: Interaction of waves with frictional interfaces using summation-by-parts difference operators: weak enforcement of nonlinear boundary conditions
cites work: Spectral methods on arbitrary grids
cites work: A skew-symmetric discontinuous Galerkin spectral element discretization and its relation to SBP-SAT finite difference methods

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (cites work)
cites work: Initial-Boundary Value Problems and the Navier-Stokes Equations

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (cites work)
cites work: A solution to the stability issues with block norm summation by parts operators

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (cites work)
cites work: Optimal diagonal-norm SBP operators

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (cites work)
cites work: Fundamental Algorithms in Computational Fluid Dynamics

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (cites work)
cites work: Steady-state computations using summation-by-parts operators

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (cites work)
cites work: Artificial dissipation models for the Euler equations

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (cites work)
cites work: On central-difference and upwind schemes

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (cites work)
cites work: Q4550823

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (cites work)
cites work: Further studies on geometric conservation law and applications to high-order finite difference schemes with stationary grids

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (cites work)
cites work: Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (cites work)
cites work: On the impact of boundary conditions on dual consistent finite difference discretizations

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (cites work)
cites work: Adjoint Consistency Analysis of Discontinuous Galerkin Discretizations

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (cites work)
cites work: Adaptive Galerkin finite element methods for partial differential equations

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (cites work)
cites work: An Entropy Adjoint Approach to Mesh Refinement

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (cites work)
cites work: Adjoint error estimation and grid adaptation for functional outputs: Application to quasi-one-dimensional flow

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (cites work)
cites work: Output error estimation for summation-by-parts finite-difference schemes

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (cites work)
cites work: A generalized framework for nodal first derivative summation-by-parts operators

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (cites work)
cites work: Skew-selfadjoint form for systems of conservation laws

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (cites work)
cites work: Q4454375

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (cites work)
cites work: A Conservative Mesh-Free Scheme and Generalized Framework for Conservation Laws

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (cites work)
cites work: Energy stable numerical methods for hyperbolic partial differential equations using overlapping domain decomposition

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (cites work)
cites work: Strict stability of high-order compact implicit finite-difference schemes: The role of boundary conditions for hyperbolic PDEs. I

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (cites work)
cites work: Strict stability of high-order compact implicit finite-difference schemes: The role of boundary conditions for hyperbolic PDEs. II

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (cites work)
cites work: Summation-by-parts in time

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (cites work)
cites work: Stable and Accurate Interpolation Operators for High-Order Multiblock Finite Difference Methods

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (cites work)
cites work: A stable and conservative method for locally adapting the design order of finite difference schemes

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (cites work)
cites work: Third-order energy stable WENO scheme

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (cites work)
cites work: A systematic methodology for constructing high-order energy stable WENO schemes

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (cites work)
cites work: Boundary closures for fourth-order energy stable weighted essentially non-oscillatory finite-difference schemes

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (DOI)
DOI: 10.1016/J.COMPFLUID.2014.02.016