253 citations · 476 across the 75 of their papers we have counts for
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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…
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…
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…
An energy-stable minimal deformation rate scheme for mean curvature flow and surface diffusion
Guangwei Gao, Harald Garcke, Buyang Li +1
We propose a new parametric finite element method, referred to as the BGN-MDR method, for simulating both mean curvature flow and surface diffusion for closed hypersurfaces, as wel…
Dynamic Ritz Projection for Finite Element Methods in Fluid-Structure Interaction
Erik Burman, Buyang Li, Rong Tang
Regardless of the development of various finite element methods for fluid-structure interaction (FSI) problems, optimal-order convergence of finite element discretizations of the F…
Optimal convergence of the arbitrary Lagrangian-Eulerian interface tracking method for two-phase Navier--Stokes flow without surface tension
Buyang Li, Shu Ma, Weifeng Qiu
Optimal-order convergence in the norm is proved for an arbitrary Lagrangian-Eulerian interface tracking finite element method for the sharp interface model of two-phase Navie…
Computing rough solutions of the stochastic nonlinear wave equation
Jiachuan Cao, Buyang Li, Katharina Schratz
The regularity of solutions to the stochastic nonlinear wave equation plays a critical role in the accuracy and efficiency of numerical algorithms. Rough or discontinuous initial c…
Maximal regularity of evolving FEMs for parabolic equations on an evolving surface
Genming Bai, Balázs Kovács, Buyang Li
In this paper, we prove that spatially semi-discrete evolving finite element method for parabolic equations on a given evolving hypersurface of arbitrary dimensions preserves the m…
Convergence of a moving window method for the Schrödinger equation with potential on
Arieh Iserles, Buyang Li, Fangyan Yao
We propose a novel framework, called moving window method, for solving the linear Schrödinger equation with an external potential in . This method employs a smooth cu…
Weak maximum principle of finite element methods for parabolic equations in polygonal domains
Genming Bai, Dmitriy Leykekhman, Buyang Li
The weak maximum principle of finite element methods for parabolic equations is proved for both semi-discretization in space and fully discrete methods with -step backward diffe…
Numerical approximation of discontinuous solutions of the semilinear wave equation
Jiachuan Cao, Buyang Li, Yanping Lin +1
A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The pr…