9 papers
Convergence of a CutFEM for fluid--structure interaction with a deforming interface
Miguel A. Fernández, Buyang Li, Maxim A. Olshanskii
We present a rigorous error analysis for a semidiscrete immersed CutFEM applied to fluid--structure interaction (FSI) problems involving an incompressible viscous fluid and an elas…
Weighted regularity of fluid-structure interaction when the interface intersects the boundary
Zhaonan Dong, Tiantian Huang, Buyang Li
This paper analyzes the regularity of solutions to a fluid-structure interaction (FSI) problem involving a Stokesian fluid and a linear elastic solid in a two-dimensional polygonal…
Convergence of Finite Element Methods for Ricci Flow
Guangwei Gao, Evan S. Gawlik, Buyang Li
The convergence of a finite element discretization for the two-dimensional Ricci flow is proved. In this method, the Ricci flow on a two-dimensional surface is formulated into solu…
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…