Volume-Preserving Parametric Finite Element Methods for Axisymmetric Geometric Evolution Equations

@article{Bao2021VolumePreservingPF,
  title={Volume-Preserving Parametric Finite Element Methods for Axisymmetric Geometric Evolution Equations},
  author={Weizhu Bao and Harald Garcke and Robert Nurnberg and Quan Zhao},
  journal={SSRN Electronic Journal},
  year={2021}
}
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6 Citations
Background Citations
2
Methods Citations
4

6 Citations

A structure-preserving parametric finite element method for area-conserved generalized mean curvature flow

We propose and analyze a structure-preserving parametric finite element method (SP-PFEM) to simulate the motion of closed curves governed by area-conserved generalized mean curvature flow in two…

A symmetrized parametric finite element method for anisotropic surface diffusion of closed curves via a Cahn-Hoffman ξ-vector formulation

Both SP-PF EM and ES-PFEM are energy dissipative and thus are unconditionally energy-stable for almost all anisotropic surface energies γ(n) arising in practical applications.

A symmetrized parametric finite element method for anisotropic surface diffusion ii. three dimensions

. For the evolution of a closed surface under anisotropic surface diffusion with a general anisotropic surface energy γ ( n ) in three dimensions (3D), where n is the unit outward normal vector, by…

A symmetrized parametric finite element method for anisotropic surface diffusion in 3D

. For the evolution of a closed surface under anisotropic surface diffusion with a general anisotropic surface energy γ ( n ) in three dimensions (3D), where n is the unit outward normal vector, by…

A structure-preserving parametric finite element method for geometric flows with anisotropic surface energy

We propose and analyze structure-preserving parametric finite element methods (SP-PFEM) for evolution of a closed curve under different geometric flows with arbitrary anisotropic surface energy 𝛾 ( 𝒏…

A convexity-preserving and perimeter-decreasing parametric finite element method for the area-preserving curve shortening flow

The convexity-preserving property of numerical schemes which approximate the anisotropic curve shortening flow is rigorously proved for the first time.

References

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