English

A space-time FEM for PDEs on evolving surfaces

Numerical Analysis 2014-03-04 v1

Abstract

The paper studies a finite element method for computing transport and diffusion along evolving surfaces. The method does not require a parametrization of a surface or an extension of a PDE from a surface into a bulk outer domain. The surface and its evolution may be given implicitly, e.g., as the solution of a level set equation. This approach naturally allows a surface to undergo topological changes and experience local geometric singularities. The numerical method uses space-time finite elements and is provably second order accurate. The paper reviews the method, error estimates and shows results for computing the diffusion of a surfactant on surfaces of two colliding droplets.

Keywords

Cite

@article{arxiv.1403.0277,
  title  = {A space-time FEM for PDEs on evolving surfaces},
  author = {Joerg Grande and Maxim Olshanskii and Arnold Reusken},
  journal= {arXiv preprint arXiv:1403.0277},
  year   = {2014}
}

Comments

arXiv admin note: text overlap with arXiv:1401.8214

R2 v1 2026-06-22T03:18:43.028Z