23 citations · 105 across the 56 of their papers we have counts for
9 papers · 1 filter
An unfitted finite element method by direct extension for elliptic problems on domains with curved boundaries and interfaces
Fanyi Yang, Xiaoping Xie
We propose and analyze an unfitted finite element method for solving elliptic problems on domains with curved boundaries and interfaces. The approximation space on the whole domain…
Optimal error estimation of a time-spectral method for fractional diffusion problems with low regularity data
Hao Luo, Xiaoping Xie
This paper is devoted to the error analysis of a time-spectral algorithm for fractional diffusion problems of order (). The solution regularity in the Sobolev space i…
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…
NFCNN: Toward a Noise Fusion Convolutional Neural Network for Image Denoising
Maoyuan Xu, Xiaoping Xie
Deep learning based methods have achieved the state-of-the-art performance in image denoising. In this paper, a deep learning based denoising method is proposed and a module called…
Semi-discrete and fully discrete HDG methods for Burgers' equation
Zimo Zhu, Gang Chen, Xiaoping Xie
This paper proposes semi-discrete and fully discrete hybridizable discontinuous Galerkin (HDG) methods for the Burgers' equation in two and three dimensions. In the spatial discret…