4 papers · 1 filter
A concurrent global-local numerical method for multiscale parabolic equations
Yulei Liao, Yang Liu, Pingbing Ming
This paper presents a concurrent global-local numerical method for solving multiscale parabolic equations in divergence form. The proposed method employs hybrid coefficient to prov…
Sharp uniform approximation for spectral Barron functions by deep neural networks
Yulei Liao, Pingbing Ming, Hao Yu
This work explores the neural network approximation capabilities for functions within the spectral Barron space , where is the smoothness index. We demonstrate t…
A broken Hardy inequality on finite element space and application to strain gradient elasticity
Yulei Liao, Pingbing Ming
We illustrate a broken Hardy inequality on discontinuous finite element spaces, blowing up with a logarithmic factor with respect to the meshes size. This is motivated by numerical…
Heterogeneous multiscale methods for fourth-order singular perturbations
Yulei Liao, Pingbing Ming
We develop a numerical homogenization method for fourth-order singular perturbation problems within the framework of heterogeneous multiscale method. These problems arise from hete…