Affiliation:
1. Dipartimento di Mathematica, Università di Trento , 38123 Trento , Italy
Abstract
AbstractWe introduce and analyse a fully discrete approximation for a mathematical model for the solidification and liquidation of materials of negligible specific heat. The model is a two-sided Mullins–Sekerka problem. The discretization uses finite elements in space and an independent parameterization of the moving free boundary. We prove unconditional stability and exact volume conservation for the introduced scheme. Several numerical simulations, including for nearly crystalline surface energies, demonstrate the practicality and accuracy of the presented numerical method.
Subject
Computational Mathematics,Numerical Analysis
Reference37 articles.
1. N. D. Alikakos, P. W. Bates and X. Chen, Convergence of the Cahn–Hilliard equation to the Hele–Shaw model, Arch. Rational Mech. Anal. 128 (1994), 165–205.
2. F. Almgren and J. E. Taylor, Flat flow is motion by crystalline curvature for curves with crystalline energies, J. Differential Geom. 42 (1995), 1–22.
3. W. Bao and Q. Zhao, A structure-preserving parametric finite element method for surface diffusion, SIAM J. Numer. Anal. 59 (2021), 2775–2799.
4. J. W. Barrett, H. Garcke and R. Nürnberg, Numerical approximation of anisotropic geometric evolution equations in the plane, IMA J. Numer. Anal. 28 (2008), 292–330.
5. J. W. Barrett, H. Garcke and R. Nürnberg, On the parametric finite element approximation of evolving hypersurfaces in R3 J. Comput. Phys. 227 (2008), 4281–4307.
Cited by
7 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献