Finite element methods for fourth order axisymmetric geometric evolution equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:376

Article

Barrett, John W.¹  Garcke, Harald²  Nurnberg, Robert¹ 

[1] Imperial Coll London, Dept Math, London SW7 2AZ, England

[2] Univ Regensburg, Fak Math, D-93040 Regensburg, Germany

关键词: Surface diffusion;    Willmore flow;    Helfrich flow;    Finite elements;    Axisymmetry;    Tangential movement;   

DOI  :  10.1016/j.jcp.2018.10.006

来源: Elsevier

【 摘 要 】

Fourth order curvature driven interface evolution equations frequently appear in the natural sciences. Often axisymmetric geometries are of interest, and in this situation numerical computations are much more efficient. We will introduce and analyze several new finite element schemes for fourth order geometric evolution equations in an axisymmetric setting, and for selected schemes we will show existence, uniqueness and stability results. The presented schemes have very good mesh and stability properties, as will be demonstrated by several numerical examples. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free