84 citations · 684 across the 49 of their papers we have counts for
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Error Inhibiting Methods for Finite Elements
Adi Ditkowski, Anne Le Blanc, Chi-Wang Shu
Finite Difference methods (FD) are one of the oldest and simplest methods for solving partial differential equations (PDE). Block Finite Difference methods (BFD) are FD methods in…
Efficient Finite Difference WENO Scheme for Hyperbolic Systems with Non-Conservative Products
Dinshaw S. Balsara, Deepak Bhoriya, Chi-Wang Shu +1
Higher order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes have been constructed for conservation laws. For multidimensional problems, they offer high order…
A primal-dual approach for solving conservation laws with implicit in time approximations
Siting Liu, Stanley Osher, Wuchen Li +1
In this work, we propose a novel framework for the numerical solution of time-dependent conservation laws with implicit schemes via primal-dual hybrid gradient methods. We solve an…
On the stability of strong-stability-preserving modified Patankar Runge-Kutta schemes
Juntao Huang, Thomas Izgin, Stefan Kopecz +2
In this paper, we perform stability analysis for a class of second and third order accurate strong-stability-preserving modified Patankar Runge-Kutta (SSPMPRK) schemes, which were…
Discontinuous Galerkin methods for stochastic Maxwell equations with multiplicative noise
Jiawei Sun, Chi-Wang Shu, Yulong Xing
In this paper we propose and analyze finite element discontinuous Galerkin methods for the one- and two-dimensional stochastic Maxwell equations with multiplicative noise. The disc…
Provably Positive Central DG Schemes via Geometric Quasilinearization for Ideal MHD Equations
Kailiang Wu, Haili Jiang, Chi-Wang Shu
In the numerical simulation of ideal MHD, keeping the pressure and density positive is essential for both physical considerations and numerical stability. This is a challenge, due…