15 citations · 139 across the 32 of their papers we have counts for
33 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…
Improving accuracy of finite element solutions by smoothing
Yuwen Li, Han Shui, Ludmil Zikatanov
This paper develops a smoothing-based postprocessing method for improving the accuracy of finite element solutions. The method applies a few smoothing iterations, such as damped Ja…
Some p-robust a posteriori error estimates based on auxiliary spaces
Yuwen Li
This work develops polynomial-degree-robust (p-robust) equilibrated a posteriori error estimates for , and problems, based on auxili…
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…
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…
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 New Convergence Analysis and Applications of POD-Greedy Algorithms
Yuwen Li, Yupeng Wang
In this article, we derive a novel convergence estimate for the weak POD-Greedy method with multiple POD modes and variable greedy thresholds in terms of the entropy numbers of the…
A new rational approximation algorithm via the empirical interpolation method
Aidi Li, Yuwen Li
We present a new rational approximation algorithm based on the empirical interpolation method for interpolating a family of parametrized functions to rational polynomials with inva…
Reduced Krylov Basis Methods for Parametric Partial Differential Equations
Yuwen Li, Ludmil T. Zikatanov, Cheng Zuo
This work is on a user-friendly reduced basis method for solving a family of parametric PDEs by preconditioned Krylov subspace methods including the conjugate gradient method, gene…
A new analysis of empirical interpolation methods and Chebyshev greedy algorithms
Yuwen Li
We present new convergence estimates of generalized empirical interpolation methods in terms of the entropy numbers of the parametrized function class. Our analysis is transparent…
A reduced conjugate gradient basis method for fractional diffusion
Yuwen Li, Ludmil T. Zikatanov, Cheng Zuo
This work is on a fast and accurate reduced basis method for solving discretized fractional elliptic partial differential equations (PDEs) of the form by rationa…
Entropy-based convergence rates of greedy algorithms
Yuwen Li, Jonathan Siegel
We present convergence estimates of two types of greedy algorithms in terms of the metric entropy of underlying compact sets. In the first part, we measure the error of a standard…
Parameter-free preconditioning for nearly-incompressible linear elasticity
James H Adler, Xiaozhe Hu, Yuwen Li +1
It is well known that via the augmented Lagrangian method, one can solve Stokes' system by solving the nearly incompressible linear elasticity equation. In this paper, we show that…
New stabilized finite element methods for nearly inviscid and incompressible flows
Yuwen Li, Ludmil Zikatanov
This work proposes a new stabilized finite element method for solving the incompressible Navier--Stokes equations. The numerical scheme is based on a reduced Bernar…
Neural networks with trainable matrix activation functions
Zhengqi Liu, Shuhao Cao, Yuwen Li +1
The training process of neural networks usually optimize weights and bias parameters of linear transformations, while nonlinear activation functions are pre-specified and fixed. Th…
Nodal auxiliary space preconditioning for the surface de Rham complex
Yuwen Li
This work develops optimal preconditioners for the discrete H(curl) and H(div) problems on two-dimensional surfaces by nodal auxiliary space preconditioning [R. Hiptmair, J. Xu: SI…
Coefficient-Robust A Posteriori Error Estimation for H(curl)-elliptic Problems
Yuwen Li
We extend the framework of a posteriori error estimation by preconditioning in [Li, Y., Zikatanov, L.: Computers \& Mathematics with Applications. \textbf{91}, 192-201 (2021)] and…
Recovery-based a posteriori error analysis for plate bending problems
Yuwen Li
We present two new recovery-based a posteriori error estimates for the Hellan--Herrmann--Johnson method in Kirchhoff--Love plate theory. The first error estimator uses a postproces…
Some continuous and discontinuous Galerkin methods and structure preservation for incompressible flows
Xi Chen, Yuwen Li, Corina Drapaca +1
In this paper, we present consistent and inconsistent discontinuous Galerkin methods for incompressible Euler and Navier-Stokes equations with the kinematic pressure, Bernoulli fun…
An Extended Galerkin analysis in finite element exterior calculus
Qingguo Hong, Yuwen Li, Jinchao Xu
For the Hodge--Laplace equation in finite element exterior calculus, we introduce several families of discontinuous Galerkin methods in the extended Galerkin framework. For contrac…
Fast auxiliary space preconditioners on surfaces
Yuwen Li
This work presents uniform preconditioners for the discrete Laplace--Beltrami operator on hypersurfaces. In particular, within the framework of fast auxiliary space preconditioning…
Nodal auxiliary a posteriori error estimates
Yuwen Li, Ludmil T. Zikatanov
We introduce and explain key relations between a posteriori error estimates and subspace correction methods viewed as preconditioners for problems in infinite dimensional Hilbert s…
A unified framework of continuous and discontinuous Galerkin methods for solving the incompressible Navier--Stokes equation
Xi Chen, Yuwen Li, Corina Drapaca +1
In this paper, we propose a unified numerical framework for the time-dependent incompressible Navier--Stokes equation which yields the -, -conforming, and disco…