23 citations · 105 across the 56 of their papers we have counts for
56 papers
Convergence of finite element approximations for the one-dimensional stochastic Burgers equation with additive trace-class noise
Binjie Li, Xiaoping Xie, Qin Zhou
This paper investigates finite element approximations of the one-dimensional viscous stochastic Burgers equation with additive trace-class noise. For the finite element spati…
A new error analysis for parabolic Dirichlet boundary control problems
Dongdong Liang, Wei Gong, Xiaoping Xie
In this paper, we consider the finite element approximation to a parabolic Dirichlet boundary control problem and establish new a priori error estimates. In the temporal semi-discr…
A New Reduced Basis Method for Parabolic Equations Based on Single-Eigenvalue Acceleration
Qijia Zhai, Qingguo Hong, Xiaoping Xie
In this paper, we develop a new reduced basis (RB) method, named as Single Eigenvalue Acceleration Method (SEAM), for second-order parabolic equations with homogeneous Dirichlet bo…
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 $…
Mixed finite element methods for the ferrofluid model with magnetization paralleled to the magnetic field
Yongke Wu, Xiaoping Xie
Mixed finite element methods are considered for a ferrofluid flow model with magnetization paralleled to the magnetic field. The ferrofluid model is a coupled system of the Maxwell…
An unfitted finite element method with direct extension stabilization for time-harmonic Maxwell problems on smooth domains
Fanyi Yang, Xiaoping Xie
We propose an unfitted finite element method for numerically solving the time-harmonic Maxwell equations on a smooth domain. The model problem involves a Lagrangian multiplier to r…