1 citations · 2 across the 11 of their papers we have counts for
11 papers
Arbitrary-order structure-preserving discretizations for geometric curvature flows
Ganghui Zhang, Boris D. Andrews, Patrick E. Farrell
Geometric flows, where an immersed manifold evolves in time according to its own geometry, exhibit important structural properties. For example, surface diffusion dissipates surfac…
Global and local helicity-preservation in the finite element discretization of magnetic relaxation
Patrick E. Farrell, Mingdong He, Kaibo Hu +1
Magnetic relaxation drives plasma toward lower-energy equilibria under helicity constraints. In ideal magnetohydrodynamics (MHD), helicity is locally conserved, while resistive the…
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…
Structure-preserving parametric finite element methods for two-phase Stokes flow based on Lagrange multiplier approaches
Harald Garcke, Dennis Trautwein, Ganghui Zhang
We present a novel formulation for parametric finite element methods to approximate two-phase Stokes flow. The new formulation is based on the classical Stokes equation in the bulk…
Isoparametric finite element methods for mean curvature flow and surface diffusion
Harald Garcke, Robert Nürnberg, Simon Praetorius +1
We propose higher-order isoparametric finite element approximations for mean curvature flow and surface diffusion. The methods are natural extensions of the piecewise linear finite…
Predictor-corrector, BGN-based parametric finite element methods for surface diffusion
Wei Jiang, Chunmei Su, Ganghui Zhang +1
We present a novel parametric finite element approach for simulating the surface diffusion of curves and surfaces. Our core strategy incorporates a predictor-corrector time-steppin…
Structure-preserving parametric finite element method for curve diffusion based on Lagrange multiplier approaches
Harald Garcke, Wei Jiang, Chunmei Su +1
We propose a novel formulation for parametric finite element methods to simulate surface diffusion of closed curves, which is also called as the curve diffusion. Several high-order…
Convergence analysis of three semi-discrete numerical schemes for nonlocal geometric flows including perimeter terms
Jiang Wei, Su Chunmei, Zhang Ganghui
We present and analyze three distinct semi-discrete schemes for solving nonlocal geometric flows incorporating perimeter terms. These schemes are based on the finite difference met…
Stable BDF time discretization of BGN-based parametric finite element methods for geometric flows
Wei Jiang, Chunmei Su, Ganghui Zhang
We propose a novel class of temporal high-order parametric finite element methods for solving a wide range of geometric flows of curves and surfaces. By incorporating the backward…
A second-order in time, BGN-based parametric finite element method for geometric flows of curves
Wei Jiang, Chunmei Su, Ganghui Zhang
Over the last two decades, the field of geometric curve evolutions has attracted significant attention from scientific computing. One of the most popular numerical methods for solv…
A convexity-preserving and perimeter-decreasing parametric finite element method for the area-preserving curve shortening flow
Wei Jiang, Chunmei Su, Ganghui Zhang
We propose and analyze a semi-discrete parametric finite element scheme for solving the area-preserving curve shortening flow. The scheme is based on Dziuk's approach (SIAM J. Nume…