253 citations · 476 across the 75 of their papers we have counts for
15 papers · 1 filter
Dynamic Ritz projection of mean curvature flow and optimal convergence of parametric FEM
Buyang Li, Rong Tang
A new approach is developed to study the convergence of parametric finite element approximations to the mean curvature flow of closed surfaces in three-dimensional space. In this a…
High-order mass-, energy- and momentum-conserving methods for the nonlinear Schrödinger equation
Georgios Akrivis, Buyang Li, Rong Tang +1
This paper introduces a novel formulation and an associated space-time finite element method for simulating solutions to the nonlinear Schrödinger equation. A major advantage of th…
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…
An least-squares UnCut FEM on domains defined by a level set function
Jiashun Hu, Buyang Li, Han Yang
We propose a novel UnCut finite element method (FEM) for the Poisson and Stokes equations on domains with curved boundaries represented by a level set function. Like the -FEM, t…
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…
High-order finite element method for perfect conductivity and linear elasticity with nearly touching inclusions
Buyang Li, Haigang Li, Yonglin Li +1
In perfect conductivity and linear elasticity problems, the electric field and stress always become highly concentrated within narrow regions between adjacent perfect (rigid) inclu…
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 exponential integration for rough solutions of nonlinear wave equations. Part II: Dynamic boundary conditions on curved domains
Jiachuan Cao, Benjamin Dörich, Buyang Li
We study nonlinear wave equations with dynamic boundary conditions on smooth bounded domains and analyze a fully discrete approximation in the low-regularity regime. The method com…
Finite element exponential integration for rough solutions of nonlinear wave equations. Part I: Dirichlet boundary conditions on polygonal and polyhedral domains
Jiachuan Cao, Benjamin Dörich, Marlis Hochbruck +1
We study a fully discrete scheme for nonlinear wave equations on general bounded polygonal/polyhedral domains with initial data , ,…
Structure-preserving Lagrange-multiplier methods for mean curvature flow and their error bounds
Balázs Kovács, Buyang Li, Christian Lubich
We propose and analyze a class of evolving surface finite element methods for mean curvature flow of closed surfaces using Lagrange multipliers for preserving the energy-decreasing…
A neural network method for scalar conservation laws with convergence rates for shock-wave solutions
Jiachuan Cao, Buyang Li, Hao Li
We propose a new entropy-compatible neural network method for scalar hyperbolic conservation laws and establish, to our knowledge, the first explicit \(L^1\) convergence rates in t…
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…