research
∙
03/30/2023
Efficient Finite Difference WENO Scheme for Hyperbolic Systems with Non-Conservative Products
Higher order finite difference Weighted Essentially Non-Oscillatory (WEN...
share
research
∙
05/03/2022
On the stability of strong-stability-preserving modified Patankar Runge-Kutta schemes
In this paper, we perform stability analysis for a class of second and t...
research
∙
04/20/2022
Discontinuous Galerkin methods for stochastic Maxwell equations with multiplicative noise
In this paper we propose and analyze finite element discontinuous Galerk...
research
∙
03/28/2022
Provably Positive Central DG Schemes via Geometric Quasilinearization for Ideal MHD Equations
In the numerical simulation of ideal MHD, keeping the pressure and densi...
research
∙
01/28/2022
Moment-based multi-resolution HWENO scheme for hyperbolic conservation laws
In this paper, a high-order moment-based multi-resolution Hermite weight...
research
∙
11/08/2021
Geometric Quasilinearization Framework for Analysis and Design of Bound-Preserving Schemes
Solutions to many partial differential equations satisfy certain bounds ...
research
∙
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...
research
∙
03/26/2021
Dissipative and conservative local discontinuous Galerkin methods for the Fornberg-Whitham type equations
In this paper, we construct high order energy dissipative and conservati...
research
∙
11/29/2020
Error Inhibiting Methods for Finite Elements
Finite Difference methods (FD) are one of the oldest and simplest method...
research
∙
09/20/2020
Cell-average WENO with progressive order of accuracy close to discontinuities with applications to signal processing
In this paper we translate to the cell-average setting the algorithm for...
research
∙
05/14/2020
A new WENO-2r algorithm with progressive order of accuracy close to discontinuities
In this article we present a modification of the algorithm for data disc...
research
∙
03/12/2020
An ultraweak-local discontinuous Galerkin method for PDEs with high order spatial derivatives
In this paper, we develop a new discontinuous Galerkin method for solvin...
research
∙
02/09/2020
Provably Physical-Constraint-Preserving Discontinuous Galerkin Methods for Multidimensional Relativistic MHD Equations
We propose and analyze a class of robust, uniformly high-order accurate ...
research
∙
01/12/2020
Sub-optimal convergence of discontinuous Galerkin methods with central fluxes for even degree polynomial approximations
In this paper, we theoretically and numerically verify that the disconti...
research
∙
01/03/2020
Error analysis of Runge–Kutta discontinuous Galerkin methods for linear time-dependent partial differential equations
In this paper, we present error estimates of fully discrete Runge–Kutta ...
research
∙
12/25/2019
Enforcing strong stability of explicit Runge–Kutta methods with superviscosity
A time discretization method is called strongly stable, if the norm of i...
research
∙
07/17/2019