3 papers
math.NA2025
Nonlinear Optimal Recovery in Hilbert Spaces
Daozhe Lin, Qiang Du
This paper investigates solution strategies for nonlinear problems in Hilbert spaces, such as nonlinear partial differential equations (PDEs) in Sobolev spaces, when only finite me…
math.NA2024
Which Spaces can be Embedded in -type Reproducing Kernel Banach Space? A Characterization via Metric Entropy
Yiping Lu, Daozhe Lin, Qiang Du
In this paper, we establish a novel connection between the metric entropy growth and the embeddability of function spaces into reproducing kernel Hilbert/Banach spaces. Metric entr…
math.NA2024
Error estimates of finite element methods for nonlocal problems using exact or approximated interaction neighborhoods
Qiang Du, Hehu Xie, Xiaobo Yin +1
We study the asymptotic error between the finite element solutions of nonlocal models with a bounded interaction neighborhood and the exact solution of the limiting local model. Th…