7 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…
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…
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…
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…