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09/17/2023
Numerical analysis of a spherical harmonic discontinuous Galerkin method for scaled radiative transfer equations with isotropic scattering
In highly diffusion regimes when the mean free path ε tends to zero, the...
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08/18/2023
On a numerical artifact of solving shallow water equations with a discontinuous bottom: Analysis and a nontransonic fix
In this paper, we study a numerical artifact of solving the nonlinear sh...
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07/12/2023
The Runge–Kutta discontinuous Galerkin method with compact stencils for hyperbolic conservation laws
In this paper, we develop a new type of Runge–Kutta (RK) discontinuous G...
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11/30/2022
High order asymptotic preserving well-balanced finite difference WENO schemes for all Mach full Euler equations with gravity
In this paper, we propose a high order semi-implicit well-balanced finit...
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05/09/2022
Energy conserving and well-balanced discontinuous Galerkin methods for the Euler-Poisson equations in spherical symmetry
This paper presents high-order Runge-Kutta (RK) discontinuous Galerkin m...
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04/20/2022
Discontinuous Galerkin methods for stochastic Maxwell equations with multiplicative noise
In this paper we propose and analyze finite element discontinuous Galerk...
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10/10/2021
Multi-symplectic discontinuous Galerkin methods for the stochastic Maxwell equations with additive noise
One- and multi-dimensional stochastic Maxwell equations with additive no...
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10/08/2021
Local discontinuous Galerkin methods for the abcd nonlinear Boussinesq system
Boussinesq type equations have been widely studied to model the surface ...
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08/10/2021
High order well-balanced asymptotic preserving finite difference WENO schemes for the shallow water equations in all Froude numbers
In this paper, high order semi-implicit well-balanced and asymptotic pre...
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06/28/2021
Finite Element Approximations of a Class of Nonlinear Stochastic Wave Equation with Multiplicative Noise
Wave propagation problems have many applications in physics and engineer...
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05/18/2021
High order finite difference Hermite WENO fixed-point fast sweeping method for static Hamilton-Jacobi equations
In this paper, we combine the nonlinear HWENO reconstruction in <cit.> a...
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04/08/2021
High order asymptotic preserving Hermite WENO fast sweeping method for the steady-state S_N transport equation
In this paper, we propose to combine the fifth order Hermite weighted es...
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09/08/2020
High order finite difference Hermite WENO fast sweeping methods for static Hamilton-Jacobi equations
In this paper, we propose a novel Hermite weighted essentially non-oscil...
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05/29/2020
Recovery of a Time-Dependent Bottom Topography Function from the Shallow Water Equations via an Adjoint Approach
We develop an adjoint approach for recovering the topographical function...
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05/14/2020
Uniformly High-Order Structure-Preserving Discontinuous Galerkin Methods for Euler Equations with Gravitation: Positivity and Well-Balancedness
This paper presents a class of novel high-order accurate discontinuous G...
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12/30/2019