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09/25/2022
A Comparative Study of Iterative Riemann Solvers for the Shallow Water and Euler Equations
The Riemann problem for first-order hyperbolic systems of partial differ...
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09/17/2021
Maximum principle preserving space and time flux limiting for Diagonally Implicit Runge-Kutta discretizations of scalar convection-diffusion equations
We provide a framework for high-order discretizations of nonlinear scala...
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03/17/2021
Numerical simulation and entropy dissipative cure of the carbuncle instability for the shallow water circular hydraulic jump
We investigate the numerical artifact known as a carbuncle, in the solut...
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02/15/2021
On the Rate of Error Growth in Time for Numerical Solutions of Nonlinear Dispersive Wave Equations
We study the numerical error in solitary wave solutions of nonlinear dis...
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09/02/2020
Bound-preserving convex limiting for high-order Runge-Kutta time discretizations of hyperbolic conservation laws
We introduce a general framework for enforcing local or global inequalit...
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05/18/2020
Entropy conservation property and entropy stabilization of high-order continuous Galerkin approximations to scalar conservation laws
This paper addresses the design of linear and nonlinear stabilization pr...
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03/26/2020
Algebraic entropy fixes and convex limiting for continuous finite element discretizations of scalar hyperbolic conservation laws
In this work, we modify a continuous Galerkin discretization of a scalar...
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09/07/2019