Finite element methods for fourth order axisymmetric geometric evolution equations

TL;DR

This paper introduces and analyzes new finite element schemes for fourth order axisymmetric geometric evolution equations, demonstrating their stability, existence, and efficiency through numerical examples.

Contribution

The paper presents novel finite element schemes specifically designed for axisymmetric fourth order geometric evolution equations, with proven stability and convergence properties.

Findings

Schemes exhibit excellent mesh and stability properties

Numerical examples confirm theoretical stability and efficiency

Existence and uniqueness results established for selected schemes

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.