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math.NA2026
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…
math.NA2026
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…
math.NA2026
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…