5 citations · 8 across the 7 of their papers we have counts for
8 papers
A constrained Onsager variational framework for parametric approximations of Willmore and Helfrich flows
Quan Zhao
We develop a constrained Onsager variational framework for parametric finite element approximations of Willmore and Helfrich flows. The weak curvature relation is used as a PDE con…
A unified energy-stable finite element approximation for evolving fluidic biomembranes
Harald Garcke, Robert Nürnberg, Quan Zhao
We present a unified finite element method for the dynamics of fluidic biomembranes. The model is governed by the Navier--Stokes equations in the bulk coupled to the surface Navier…
A minimizing-movement framework for geometric gradient flows with admissible tangential motion
Xiaoxiao Liu, Quan Zhao
We develop a minimizing-movement framework for parametric finite element approximations of geometric gradient flows with admissible tangential motion. At each time step, the discre…
Geometric structure-preserving parametric finite element approximations for the constrained Helfrich flow
Xiaoxiao Liu, Quan Zhao
We propose a structure-preserving parametric finite element method for the constrained Helfrich flow of closed curves and surfaces. The proposed method is based on a two-stage velo…
Thermodynamically Consistent Modeling and Stable ALE Approximations of Reactive Semi-Permeable Interfaces
Weidong Shi, Shixin Xu, Zhen Zhang +1
Reactive, semi-permeable interfaces play important roles in key biological processes such as targeted drug delivery, lipid metabolism, and signal transduction. These systems involv…
An energy-stable parametric finite element method for Willmore flow with normal-tangential velocity splitting
Harald Garcke, Robert Nürnberg, Quan Zhao
We propose and analyze an energy-stable fully discrete parametric approximation for Willmore flow of hypersurfaces in two and three space dimensions. We allow for the presence of s…
Stable fully practical finite element methods for axisymmetric Willmore flow
Harald Garcke, Robert Nürnberg, Quan Zhao
We consider fully discrete numerical approximations for axisymmetric Willmore flow that are unconditionally stable and work reliably without remeshing. We restrict our attention to…
Stable fully discrete finite element methods with BGN tangential motion for Willmore flow of planar curves
Harald Garcke, Robert Nürnberg, Quan Zhao
We propose and analyze stable finite element approximations for Willmore flow of planar curves. The presented schemes are based on a novel weak formulation which combines an evolut…