7 citations · 32 across the 23 of their papers we have counts for
23 papers
Pathwise uniform convergence of numerical approximations for a two-dimensional stochastic Navier-Stokes equation with no-slip boundary conditions
Binjie Li, Xiaoping Xie, Qin Zhou
This paper investigates the pathwise uniform convergence in probability of fully discrete finite-element approximations for the two-dimensional stochastic Navier-Stokes equations w…
Stability and convergence of the Euler scheme for stochastic linear evolution equations in Banach spaces
Binjie Li, Xiaoping Xie
For the Euler scheme of the stochastic linear evolution equations, discrete stochastic maximal -regularity estimate is established, and a sharp error estimate in the norm $…
Temporal semi-discretizations of a backward semilinear stochastic evolution equation
Binjie Li, Xiaoping Xie
This paper studies the convergence of three temporal semi-discretizations for a backward semilinear stochastic evolution equation. For general terminal value and general coefficien…
Convergence of a spatial semi-discretization for a backward semilinear stochastic parabolic equation
Binjie Li, Xiaoping Xie
This paper studies the convergence of a spatial semi-discretization for a backward semilinear stochastic parabolic equation. The filtration is general, and the spatial semi-discret…
L1 scheme for solving an inverse problem subject to a fractional diffusion equation
Binjie Li, Xiaoping Xie, Yubin Yan
This paper considers the temporal discretization of an inverse problem subject to a time fractional diffusion equation. Firstly, the convergence of the L1 scheme is established wit…
Numerical analysis of two Galerkin discretizations with graded temporal grids for fractional evolution equations
Binjie Li, Tao Wang, Xiaoping Xie
Two numerical methods with graded temporal grids are analyzed for fractional evolution equations. One is a low-order discontinuous Galerkin (DG) discretization in the case of fract…
Discontinuous Galerkin method for a distributed optimal control problem governed by a time fractional diffusion equation
Tao Wang, Binjie Li, Xiaoping Xie
This paper is devoted to the numerical analysis of a control constrained distributed optimal control problem subject to a time fractional diffusion equation with non-smooth initial…
Numerical analysis of a semilinear fractional diffusion equation
Binjie Li, Tao Wang, Xiaoping Xie
This paper considers the numerical analysis of a semilinear fractional diffusion equation with nonsmooth initial data. A new Grönwall's inequality and its discrete version are prop…
Analysis of a time-stepping discontinuous Galerkin method for fractional diffusion-wave equation with nonsmooth data
Binjie Li, Tao Wang, Xiaoping Xie
This paper analyzes a time-stepping discontinuous Galerkin method for fractional diffusion-wave problems. This method uses piecewise constant functions in the temporal discretizati…
Analysis of the L1 scheme for fractional wave equations with nonsmooth data
Binjie Li, Tao Wang, Xiaoping Xie
This paper analyzes the well-known L1 scheme for fractional wave equations with nonsmooth data. A new stability estimate is obtained, and the temporal accuracy $ \mathcal O(τ^{3-α}…
Convergence analysis of a Petrov-Galerkin method for fractional wave problems with nonsmooth data
Hao Luo, Binjie Li, Xiaoping Xie
This paper analyzes the convergence of a Petrov-Galerkin method for time fractional wave problems with nonsmooth data. Well-posedness and regularity of the weak solution to the tim…
Error estimation of a discontinuous Galerkin method for time fractional subdiffusion problems with nonsmooth data
Binjie Li, Hao Luo, Xiaoping Xie
This paper is devoted to the numerical analysis of a piecewise constant discontinuous Galerkin method for time fractional subdiffusion problems. The regularity of weak solution is…
Analysis of a time-stepping scheme for time fractional diffusion problems with nonsmooth data
Binjie Li, Hao Luo, Xiaoping Xie
This paper establishes the convergence of a time-steeping scheme for time fractional diffusion problems with nonsmooth data. We first analyze the regularity of the model problem wi…
A space-time finite element method for fractional wave problems
Binjie Li, Hao Luo, Xiaoping Xie
This paper analyzes a space-time finite element method for fractional wave problems. The method uses a Petrov-Galerkin type time-stepping scheme to discretize the time fractional d…
Analysis of a time-stepping discontinuous Galerkin method for modified anomalous subdiffusion problems
Binjie Li, Hao Luo, Xiaoping Xie
This paper analyzes a time-stepping discontinuous Galerkin method for modified anomalous subdiffusion problems with two time fractional derivatives of orders and ($ 0 < α…
A time-spectral algorithm for fractional wave problems
Binjie Li, Hao Luo, Xiaoping Xie
This paper develops a high-accuracy algorithm for time fractional wave problems, which employs a spectral method in the temporal discretization and a finite element method in the s…
Regularity for time fractional wave problems
Binjie Li, Xiaoping Xie
Using the Galerkin method, we obtain the unique existence of the weak solution to a time fractional wave problem, and establish some regularity estimates which reveal the singulari…
Regularity of solutions to time fractional diffusion equations
Binjie Li, Xiaoping Xie
We derive some regularity estimates of the solution to a time fractional diffusion equation, that are useful for numerical analysis, and partially unravel the singularity structure…
A new smoothness result for Caputo-type fractional ordinary differential equations
Binjie Li, Xiaoping Xie, Shiquan Zhang
We present a new smoothness result for Caputo-type fractional ordinary differential equations, which reveals that, subtracting a non-smooth function that can be obtained by the inf…
Analysis of a two-level algorithm for HDG methods for diffusion problems
Binjie Li, Xiaoping Xie, Shiquan Zhang
This paper analyzes an abstract two-level algorithm for hybridizable discontinuous Galerkin (HDG) methods in a unified fashion. We use an extended version of the Xu-Zikatanov (X-Z)…
BPX preconditioner for nonstandard finite element methods for diffusion problems
Binjie Li, Xiaoping Xie
This paper proposes and analyzes an optimal preconditioner for a general linear symmetric positive definite (SPD) system by following the basic idea of the well-known BPX framework…
Analysis of a family of HDG methods for second order elliptic problems
Binjie Li, Xiaoping Xie
In this paper, we analyze a family of hybridizable discontinuous Galerkin (HDG) methods for second order elliptic problems in two and three dimensions. The methods use piecewise po…
A two-level algorithm for the weak Galerkin discretization of diffusion problems
Binjie Li, Xiaoping Xie
This paper analyzes a two-level algorithm for the weak Galerkin (WG) finite element methods based on local Raviart-Thomas (RT) and Brezzi-Douglas-Marini (BDM) mixed elements for tw…