English

Finite element methods for fourth order axisymmetric geometric evolution equations

Numerical Analysis 2019-02-13 v2

Abstract

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.

Keywords

Cite

@article{arxiv.1806.05093,
  title  = {Finite element methods for fourth order axisymmetric geometric evolution equations},
  author = {John W. Barrett and Harald Garcke and Robert Nürnberg},
  journal= {arXiv preprint arXiv:1806.05093},
  year   = {2019}
}

Comments

Revised version. 37 pages, 27 figures. This article is closely related to arXiv:1805.04322

R2 v1 2026-06-23T02:28:50.082Z