四阶轴对称几何演化方程的有限元方法
Finite element methods for fourth order axisymmetric geometric evolution equations
AI总结：
本文研究了四阶轴对称几何演化方程的有限元方法，提出并分析了几种新的有限元方案，并对选定方案展示了存在性、唯一性和稳定性结果，通过数值例子验证了网格和稳定性特性。
摘要：
四阶曲率驱动界面演化方程在自然科学中经常出现。在这种情况 下，轴对称几何往往具有兴趣，此时数值计算更加高效。我们将介绍并分析几种新的四阶几何演化方程在轴对称设置下的有限元方案，并对选定方案展示存在性、唯一性和稳定性结果。所提出的方案具有很好的网格和稳定性特性，这将通过几个数值例子来展示。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
