This article develops a new discontinuous Galerkin (DG) method on structured meshes for
solving shallow water equations. The method here applies the one-stage ADER (Arbitrary …

由于映射操作会带来额外的计算时间消耗, 传统加映射的WENO 格式存在计算效率低的缺陷.
为了提高传统加映射WENO 格式的计算效率, 通过利用标准符号函数的一种近似逼近函数构造 …

本文针对具有不规则几何形状和非平坦底地形的浅水波方程, 引入了保正高阶ADER
间断Galerkin 方法, 该方法能准确地保持静水的稳态. 为了满足well-balanced 的性质 …

本文提出了求解非守恒双曲型偏微分方程的一种新的路径守恒间断Galerkin (DG) 方法. 特别地,
这里的方法采用了一级ADER (在空间和时间的任意导数) 方法来实现时间离散化. 此外 …

This article develops a new discontinuous Galerkin (DG) method with the one-stage arbitrary
derivatives in time and space approach to solve one-dimensional hyperbolic conservation …

The traditional mapped weighted essentially non-oscillatory (WENO) schemes commonly
suffer from the drawback of low-efficiency, since they usually require the mapping processes …

本文提出了一种全新的间断Galerkin (DG) 方法, 该方法使用单级ADER (任意时–空导数)
方式进行时间离散. 该方法利用微分变换步骤递归地将解的时–空展开系数通过低阶空间展开 …

This article develops a new well-balanced discontinuous Galerkin method for the shallow
water flows in channels with irregular geometry and over uneven bottom topography, which …

In this article, we propose a new path-conservative discontinuous Galerkin (DG) method to
solve the non-conservative hyperbolic partial differential equations (PDE). In particular, the …

The numerical resolution of Hamilton–Jacobi (HJ) and Hamilton–Jacobi–Bellman (HJB)
equations is performed using the Space-Time Isogeometric Discontinuous Galerkin Method …