84 citations · 684 across the 49 of their papers we have counts for
7 papers · 1 filter
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…
Cell-average WENO with progressive order of accuracy close to discontinuities with applications to signal processing
Sergio Amat, Juan Ruiz, Chi-Wang Shu +1
In this paper we translate to the cell-average setting the algorithm for the point-value discretization presented in S. Amat, J. Ruiz, C.-W. Shu, D. F. Yáñez, A new WENO-2r algorit…
A new WENO-2r algorithm with progressive order of accuracy close to discontinuities
Sergio Amat, Juan Ruiz, Chi-Wang Shu +1
In this article we present a modification of the algorithm for data discretized in the point values introduced in [S. Amat, J. Ruiz, C.-W. Shu, On a new WENO algorithm of order 2r…
An ultraweak-local discontinuous Galerkin method for PDEs with high order spatial derivatives
Qi Tao, Yan Xu, Chi-Wang Shu
In this paper, we develop a new discontinuous Galerkin method for solving several types of partial differential equations (PDEs) with high order spatial derivatives. We combine the…
Sub-optimal convergence of discontinuous Galerkin methods with central fluxes for linear hyperbolic equations with even degree polynomial approximations
Yong Liu, Chi-Wang Shu, Mengping Zhang
In this paper, we theoretically and numerically verify that the discontinuous Galerkin (DG) methods with central fluxes for linear hyperbolic equations on non-uniform meshes have s…
Provably Physical-Constraint-Preserving Discontinuous Galerkin Methods for Multidimensional Relativistic MHD Equations
Kailiang Wu, Chi-Wang Shu
We propose and analyze a class of robust, uniformly high-order accurate discontinuous Galerkin (DG) schemes for multidimensional relativistic magnetohydrodynamics (RMHD) on general…
Error analysis of Runge--Kutta discontinuous Galerkin methods for linear time-dependent partial differential equations
Zheng Sun, Chi-Wang Shu
In this paper, we present error estimates of fully discrete Runge--Kutta discontinuous Galerkin (DG) schemes for linear time-dependent partial differential equations. The analysis…