A fully discrete curve-shortening polygonal evolution law for moving boundary problems
From MaRDI portal
Publication:2123913
DOI10.1016/j.jcp.2020.109857OpenAlexW3088218314MaRDI QIDQ2123913
Yuto Miyatake, Koya Sakakibara
Publication date: 14 April 2022
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1912.00545
moving boundary problemsgeometric numerical integrationdiscrete gradient methodtangential redistribution
Related Items (2)
A Convexity-Preserving and Perimeter-Decreasing Parametric Finite Element Method for the Area-Preserving Curve Shortening Flow ⋮ A simple numerical method for Hele-Shaw type problems by the method of fundamental solutions
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Polygonal Hele-Shaw problem with surface tension
- A general framework for finding energy dissipative/conservative \(H^1\)-Galerkin schemes and their underlying \(H^1\)-weak forms for nonlinear evolution equations
- Linear energy-preserving integrators for Poisson systems
- Evolution of plane curves with a curvature adjusted tangential velocity
- Dissipative/conservative Galerkin method using discrete partial derivatives for nonlinear evolution equations
- The heat equation shrinking convex plane curves
- The heat equation shrinks embedded plane curves to round points
- Accurate numerical scheme for the flow by curvature
- Removing the stiffness from interfacial flows with surface tension
- Numerical analysis of moving boundary problems using the boundary tracking method
- Energy dissipative numerical schemes for gradient flows of planar curves
- Finite difference schemes for \(\frac{\partial u}{\partial t}=(\frac{\partial}{\partial x})^\alpha\frac{\delta G}{\delta u}\) that inherit energy conservation or dissipation property
- Preserving energy resp. dissipation in numerical PDEs using the ``Average Vector Field method
- Conformal and potential analysis in Hele-Shaw cells.
- Gage's original normalized CSF can also yield the Grayson theorem
- Time integration and discrete Hamiltonian systems
- Stability of Runge-Kutta Methods for Trajectory Problems
- The approximation of planar curve evolutions by stable fully implicit finite element schemes that equidistribute
- Discrete Variational Derivative Method
- Topics in structure-preserving discretization
- Numerical Solution of Constrained Curvature Flow for Closed Planar Curves
- Numerical Studies of Discrete Approximations to the Allen–Cahn Equation in the Sharp Interface Limit
- A direct method for solving an anisotropic mean curvature flow of plane curves with an external force
- Evolution of curves on a surface driven by the geodesic curvature and external force
- Energy-diminishing integration of gradient systems
- A new class of energy-preserving numerical integration methods
- Geometric Numerical Integration
- A Characterization of Energy-Preserving Methods and the Construction of Parallel Integrators for Hamiltonian Systems
- Numerical Methods for Ordinary Differential Equations
- Solving ODEs numerically while preserving a first integral
This page was built for publication: A fully discrete curve-shortening polygonal evolution law for moving boundary problems
