8 papers · 1 filter
Construction and Optimization of Summation-by-Parts Operators for General Function Spaces Using an Improved Generalized Gaussian Quadrature Algorithm
Alex Bercik, Lisa Patrascu, David W. Zingg
We construct optimized summation-by-parts (SBP) operators for general function spaces with provably minimal degrees of freedom on open, closed, and half-open nodal distributions. T…
On the Practical Impact of Local Linear Instabilities in Entropy-Stable Schemes
Alex Bercik, David W. Zingg
Local linear instability refers to the linearized discrete operator exhibiting perturbation growth exceeding that of the corresponding continuous linearized problem. In the context…
Convergence of entropy-stable continuous summation-by-parts discretizations of symmetric hyperbolic conservation laws
Zelalem Arega Worku, David C. Del Rey Fernández, David W. Zingg
The Lax equivalence theorem guarantees convergence of stable and consistent discretizations for linear hyperbolic partial differential equations (PDEs). For nonlinear problems, how…
Stable Volume Dissipation for High-Order Finite-Difference and Spectral-Element Methods with the Summation-by-Parts Property
Alex Bercik, David A. Craig Penner, David W. Zingg
The construction of stable, conservative, and accurate volume dissipation is extended to discretizations that possess a generalized summation-by-parts (SBP) property within a tenso…
Very high-order symmetric positive-interior quadrature rules on triangles and tetrahedra
Zelalem Arega Worku, Jason E. Hicken, David W. Zingg
We present novel fully-symmetric quadrature rules with positive weights and strictly interior nodes of degrees up to 84 on triangles and 40 on tetrahedra. Initial guesses for solvi…
Efficient Entropy-Stable Discontinuous Spectral-Element Methods Using Tensor-Product Summation-by-Parts Operators on Triangles and Tetrahedra
Tristan Montoya, David W. Zingg
We present a new class of efficient and robust discontinuous spectral-element methods of arbitrary order for nonlinear hyperbolic systems of conservation laws on curved triangular…