7 citations · 13 across the 18 of their papers we have counts for
29 papers
Dual formulations of geometric curvature flows and their discretizations
Guangwei Gao, Buyang Li, Rong Tang
We propose new formulations of geometric curvature flows -- referred to as \emph{dual formulations} -- that are equivalent to the original formulations but provide a novel framewor…
Finite element methods for isometric embedding of Riemannian manifolds
Guangwei Gao, Kaibo Hu, Buyang Li +1
The isometric embedding problem for Riemannian manifolds, which connects intrinsic and extrinsic geometry, is a central question in differential geometry with deep theoretical sign…
A convergent finite element method with minimal deformation rate for mean curvature flow
Tiantian Huang, Buyang Li, Rong Tang
We propose and analyze a fully discrete parametric finite element method with minimal deformation rate (MDR) for simulating the mean curvature flow of general closed surfaces in th…
An inertial minimal-deformation-rate framework for shape optimization
Falai Chen, Buyang Li, Jiajie Li +1
We propose a robust numerical framework for PDE-constrained shape optimization and Willmore-driven surface hole filling. To address two central challenges -- slow progress in flat…
Numerical analysis of 2D Navier--Stokes equations with nonsmooth initial value in the critical space
Buyang Li, Qiqi Rao, Hui Zhang +1
This paper addresses the numerical solution of the two-dimensional Navier--Stokes (NS) equations with nonsmooth initial data in the space, which is the critical space for the…
Computing rough solutions of the KdV equation below
Jiachuan Cao, Buyang Li, Yifei Wu +1
We establish a novel numerical and analytical framework for solving the Korteweg--de Vries (KdV) equation in the negative Sobolev spaces, where classical numerical methods fail due…