Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations
Abstract Summation-by-parts (SBP) operators have a number of properties that make them
an attractive option for higher-order spatial discretizations of partial differential equations. In …
an attractive option for higher-order spatial discretizations of partial differential equations. In …
Review of summation-by-parts schemes for initial–boundary-value problems
High-order finite difference methods are efficient, easy to program, scale well in multiple
dimensions and can be modified locally for various reasons (such as shock treatment for …
dimensions and can be modified locally for various reasons (such as shock treatment for …
Entropy stable space–time discontinuous Galerkin schemes with summation-by-parts property for hyperbolic conservation laws
L Friedrich, G Schnücke, AR Winters… - Journal of Scientific …, 2019 - Springer
This work examines the development of an entropy conservative (for smooth solutions) or
entropy stable (for discontinuous solutions) space–time discontinuous Galerkin (DG) method …
entropy stable (for discontinuous solutions) space–time discontinuous Galerkin (DG) method …
Reinterpretation and extension of entropy correction terms for residual distribution and discontinuous Galerkin schemes: application to structure preserving …
For the general class of residual distribution (RD) schemes, including many finite element
(such as continuous/discontinuous Galerkin) and flux reconstruction methods, an approach …
(such as continuous/discontinuous Galerkin) and flux reconstruction methods, an approach …
Analysis of the SBP-SAT stabilization for finite element methods part II: entropy stability
In the hyperbolic research community, there exists the strong belief that a continuous
Galerkin scheme is notoriously unstable and additional stabilization terms have to be added …
Galerkin scheme is notoriously unstable and additional stabilization terms have to be added …
New time-marching methods for compressible Navier-Stokes equations with applications to aeroacoustics problems
This paper derives a new class of time-marching methods of Runge-Kutta type (CERK) for
the simulations of the two and three-dimensional compressible Navier-Stokes equations …
the simulations of the two and three-dimensional compressible Navier-Stokes equations …
Summation-by-parts operators for general function spaces: The second derivative
Many applications rely on solving time-dependent partial differential equations (PDEs) that
include second derivatives. Summation-by-parts (SBP) operators are crucial for develo** …
include second derivatives. Summation-by-parts (SBP) operators are crucial for develo** …
[HTML][HTML] Multi-dimensional summation-by-parts operators for general function spaces: Theory and construction
Abstract Summation-by-parts (SBP) operators allow us to systematically develop energy-
stable and high-order accurate numerical methods for time-dependent differential equations …
stable and high-order accurate numerical methods for time-dependent differential equations …
Summation-by-parts operators for general function spaces
Summation-by-parts (SBP) operators are popular building blocks for systematically
develo** stable and high-order accurate numerical methods for time-dependent …
develo** stable and high-order accurate numerical methods for time-dependent …
The SBP-SAT technique for initial value problems
T Lundquist, J Nordström - Journal of Computational Physics, 2014 - Elsevier
A detailed account of the stability and accuracy properties of the SBP-SAT technique for
numerical time integration is presented. We show how the technique can be used to …
numerical time integration is presented. We show how the technique can be used to …