11 papers
Nearly optimal Kolmogorov widths under holomorphic mappings
Yuwen Li, Guozhi Zhang
This paper establishes essentially optimal asymptotic bounds for Kolmogorov widths under holomorphic mappings between complex Banach spaces. Given a compact parameter set whose Kol…
An Adaptive Finite Element Method Based on Generalized Barycentric Coordinates
Yihui Zhou, Yuwen Li
This work derives a posteriori error estimate of polygonal finite element methods based on Wachspress barycentric coordinates. In particular, we prove that the classical residual-b…
Superconvergence in finite element method by smoothing
Yuwen Li, Han Shui, Ludmil Zikatanov
This paper develops a smoothing-based postprocessing method for superconvergence in finite element methods. The method applies a few smoothing iterations, such as damped Jacobi, Ga…
Higher Order Approximation Rates for ReLU CNNs in Korobov Spaces
Yuwen Li, Guozhi Zhang
This paper investigates the approximation error for higher order Korobov functions using deep convolutional neural networks (CNNs) with ReLU activation. For target functions…
Some Super-approximation Rates of ReLU Neural Networks for Korobov Functions
Yuwen Li, Guozhi Zhang
This paper examines the and norm approximation errors of ReLU neural networks for Korobov functions. In terms of network width and depth, we derive nearly optimal sup…
Smoother-type a posteriori error estimates for finite element methods
Yuwen Li, Han Shui
This work develops user-friendly a posteriori error estimates of finite element methods, based on smoothers of linear iterative solvers. The proposed method employs simple smoother…