Numerical simulation and linear well-posedness analysis for a class of three-phase boundary motion problems

Pan, Zhenguo; Wetton, Brian

doi:10.1016/j.cam.2012.02.013

Cited by 3 publications

(1 citation statement)

References 31 publications

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“…The idea of using (1.6) instead to simulate curves forming networks was picked up in [8] and further investigated in subsequent work [25]. Finite difference techniques were used for the PDE and the triple junction condition (1.2).…”

Section: P Pozzi and B Stinnermentioning

confidence: 99%

On motion by curvature of a network with a triple junction

Pozzi¹,

Stinner²

2021

The SMAI Journal of Computational Mathematics

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We numerically study the planar evolution by curvature flow of three parametrised curves that are connected by a triple junction in which conditions are imposed on the angles at which the curves meet. One of the key problems in analysing motion of networks by curvature law is the choice of a tangential velocity that allows for motion of the triple junction, does not lead to mesh degeneration, and is amenable to an error analysis. Our approach consists in considering a perturbation of a classical smooth formulation. The problem we propose admits a natural variational formulation that can be discretized with finite elements. The perturbation can be made arbitrarily small when a regularisation parameter shrinks to zero. Convergence of the new semi-discrete finite element scheme including optimal error estimates are proved. These results are supported by some numerical tests. Finally, the influence of the small regularisation parameter on the properties of scheme and the accuracy of the results is numerically investigated.

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Section: P Pozzi and B Stinnermentioning

confidence: 99%