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08/28/2023
Consistency and convergence of flux-corrected finite element methods for nonlinear hyperbolic problems
We investigate the consistency and convergence of flux-corrected finite ...
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03/01/2023
Monolithic Convex Limiting for Legendre-Gauss-Lobatto Discontinuous Galerkin Spectral Element Methods
We extend the monolithic convex limiting (MCL) methodology to nodal disc...
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12/29/2022
Dissipation-based WENO stabilization of high-order finite element methods for scalar conservation laws
We present a new perspective on the use of weighted essentially nonoscil...
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07/15/2022
Bound-preserving and entropy-stable algebraic flux correction schemes for the shallow water equations with topography
A well-designed numerical method for the shallow water equations (SWE) s...
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12/14/2021
An unfitted finite element method using level set functions for extrapolation into deformable diffuse interfaces
We explore a new way to handle flux boundary conditions imposed on level...
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10/29/2021
An Assessment of Solvers for Algebraically Stabilized Discretizations of Convection-Diffusion-Reaction Equations
We consider flux-corrected finite element discretizations of 3D convecti...
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10/19/2021
Optimal control using flux potentials: A way to construct bound-preserving finite element schemes for conservation laws
To ensure preservation of local or global bounds for numerical solutions...
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07/23/2021
Limiter-based entropy stabilization of semi-discrete and fully discrete schemes for nonlinear hyperbolic problems
The algebraic flux correction (AFC) schemes presented in this work const...
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04/12/2021
Analysis of algebraic flux correction for semi-discrete advection problems
We present stability and error analysis for algebraic flux correction sc...
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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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08/27/2020
A new perspective on flux and slope limiting in discontinuous Galerkin methods for hyperbolic conservation laws
In this work, we discuss and develop multidimensional limiting technique...
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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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04/07/2020
Entropy stabilization and property-preserving limiters for discontinuous Galerkin discretizations of nonlinear hyperbolic equations
The methodology proposed in this paper bridges the gap between entropy s...
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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
