4 papers
A well-balanced oscillation-free discontinuous Galerkin method for shallow water equations
Yong Liu, Jianfang Lu, Qi Tao +1
In this paper, we develop a well-balanced oscillation-free discontinuous Galerkin (OFDG) method for solving the shallow water equations with a non-flat bottom topography. One notab…
Discontinuous Galerkin methods for the Ostrovsky-Vakhnenko equation
Qian Zhang, Yinhua Xia
In this paper, we develop discontinuous Galerkin (DG) methods for the Ostrovsky-Vakhnenko (OV) equation, which yields the shock solutions and singular soliton solutions, such as pe…
Discontinuous Galerkin methods for short pulse type equations via hodograph transformations
Qian Zhang, Yinhua Xia
In the present paper, we consider the discontinuous Galerkin (DG) methods for solving short pulse (SP) type equations. The short pulse equation has been shown to be completely inte…
Binary black hole simulation with an adaptive finite element method II: Application of local discontinuous Galerkin method to Einstein equations
Zhoujian Cao, Pei Fu, Li-Wei Ji +1
Finite difference method and pseudo-spectral method have been widely used in the numerical relativity to solve the Einstein equations. As the third major category method to solve p…