51 citations · 135 across the 19 of their papers we have counts for
19 papers
Multiple-GPU accelerated high-order gas-kinetic scheme on three-dimensional unstructured meshes
Yuhang Wang, Waixiang Cao, Liang Pan
Recently, successes have been achieved for the high-order gas-kinetic schemes (HGKS) on unstructured meshes for compressible flows. In this paper, to accelerate the computation, HG…
An Oscillation-free Spectral Volume Method for Hyperbolic Conservation Laws
Xinyue Zhang, Waixiang Cao, Liang Pan
In this paper, an oscillation-free spectral volume (OFSV) method is proposed and studied for the hyperbolic conservation laws. The numerical scheme is designed by introducing a dam…
Two types of spectral volume methods for 1-D linear hyperbolic equations with degenerate variable coefficients
Minqiang Xu, Yanting yuan, Waixiang Cao +1
In this paper, we analyze two classes of spectral volume (SV) methods for one-dimensional hyperbolic equations with degenerate variable coefficients. The two classes of SV methods…
An - Primal-Dual Weak Galerkin method for div-curl Systems
Waixiang Cao, Chunmei Wang, Junping Wang
This paper presents a new -primal-dual weak Galerkin (PDWG) finite element method for the div-curl system with the normal boundary condition for . Two crucial features fo…
An - Primal-Dual Weak Galerkin Method for Convection-Diffusion Equations
Waixiang Cao, Chunmei Wang, Junping Wang
In this article, the authors present a new - primal-dual weak Galerkin method (-PDWG) for convection-diffusion equations with . The existence and uniqueness of the n…
Superconvergence of the Direct Discontinuous Galerkin Method for Two-Dimensional Nonlinear Convection-Diffusion Equations
Xinyue Zhang, Waixiang Cao
This paper is concerned with superconvergence properties of the direct discontinuous Galerkin (DDG) method for two-dimensional nonlinear convection-diffusion equations. By using th…
An -weak Galerkin method for second order elliptic equations in non-divergence form
Waixiang Cao, Junping Wang, Yuesheng Xu
This article presents a new primal-dual weak Galerkin method for second order elliptic equations in non-divergence form. The new method is devised as a constrained -optimizati…
A -conforming Petrov-Galerkin method for convection-diffusion equations and superconvergence ananlysis over rectangular meshes
Waixiang Cao, Lueling Jia, Zhimin Zhang
In this paper, a new -conforming Petrov-Galerkin method for convection-diffusion equations is designed and analyzed. The trail space of the proposed method is a -conformi…
Unconditionally optimal convergence of an energy-conserving and linearly implicit scheme for nonlinear wave equations
Waixiang Cao, Dongfang Li, Zhimin Zhang
In this paper, we present and analyze an energy-conserving and linearly implicit scheme for solving the nonlinear wave equations. Optimal error estimates in time and superconvergen…
A New Primal-Dual Weak Galerkin Method for Elliptic Interface Problems with Low Regularity Assumptions
Waixiang Cao, Chunmei Wang, Junping Wang
This article introduces a new primal-dual weak Galerkin (PDWG) finite element method for second order elliptic interface problems with ultra-low regularity assumptions on the exact…
A Petrov-Galerkin method and Gauss collocation method for 1D general elliptic problems and superconvergence
Waixiang Cao, Lueling Jia, Zhimin Zhang
In this paper, we present and study Petrov-Galerkin and Gauss collocation methods with arbitrary polynomial degree () for one-dimensional elliptic equations. We pr…
New Primal-Dual Weak Galerkin Finite Element Methods for Convection-Diffusion Problems
Waixiang Cao, Chunmei Wang
This article devises a new primal-dual weak Galerkin finite element method for the convection-diffusion equation. Optimal order error estimates are established for the primal-dual…
An Accurate and Efficient Algorithm for The Time-fractional Molecular Beam Epitaxy Model with Slope Selection
Lizhen Chen, Jia Zhao, Waixiang Cao +2
In this paper, we propose a time-fractional molecular beam epitaxy (MBE) model with slope selection and its efficient, accurate, full discrete, linear numerical approximation. The…
Superconvergence of immersed finite volume methods for one-dimensional interface problems
Waixiang Cao, Xu Zhang, Zhimin Zhang +1
In this paper, we introduce a class of high order immersed finite volume methods (IFVM) for one-dimensional interface problems. We show the optimal convergence of IFVM in H1 and L2…
Superconvergence of Immersed Finite Element Methods for Interface Problems
Waixiang Cao, Xu Zhang, Zhimin Zhang
In this article, we study superconvergence properties of immersed finite element methods for the one dimensional elliptic interface problem. Due to low global regularity of the sol…
Superconvergence of Local Discontinuous Galerkin method for one-dimensional linear parabolic equations
Waixiang Cao, Zhimin Zhang
In this paper, we study superconvergence properties of the local discontinuous Galerkin method for one-dimensional linear parabolic equations when alternating fluxes are used. We p…
Is -Conjecture valid for finite volume methods?
Waixiang Cao, Zhimin Zhang, Qingsong Zou
This paper is concerned with superconvergence properties of a class of finite volume methods of arbitrary order over rectangular meshes. Our main result is to prove {\it 2k-conject…
Superconvergence of Discontinuous Galerkin method for linear hyperbolic equations
Cao Waixiang, Zhang Zhimin, Zou Qingsong
In this paper, we study superconvergence properties of the discontinuous Galerkin (DG) method for one-dimensional linear hyperbolic equation when upwind fluxes are used. We prove,…
Any order superconvergence finite volume schemes for 1D general elliptic equations
Waixiang Cao, Zhimin Zhang, Qingsong Zou
We present and analyze a finite volume scheme of arbitrary order for elliptic equations in the one-dimensional setting. In this scheme, the control volumes are constructed by using…