Finite element methods for fourth order axisymmetric geometric evolution equations
It provides efficient numerical methods for solving fourth order curvature-driven interface evolution problems in axisymmetric geometries, which are common in natural sciences.
The paper develops new finite element schemes for fourth order axisymmetric geometric evolution equations, proving existence, uniqueness, and stability for selected schemes, and demonstrating good mesh and stability properties through numerical examples.
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.