论文标题
在不断发展的表面上的部分微分方程的准确且坚固的欧拉有限元方法
An Accurate and Robust Eulerian Finite Element Method for Partial Differential Equations on Evolving Surfaces
论文作者
论文摘要
在本文中，我们提出了一种新的Eulerian有限元方法，用于在不断发展的表面上离散标量部分微分方程。在这种方法中，我们使用标准时空有限元元件空间限制到时空表面上。该方法的结构使其自然拟合到不断发展的表面的水平集表示。该方法的高阶版本基于文献中为固定表面开发的网格变形的时空变体。我们提出的离散方法是（最佳）高阶精度，可通过足够平滑的解决方案平稳变化。没有任何修改，该方法可用于离散拓扑奇异性问题。一项数值研究表明，相对于综合奇异性，平滑病例的高阶精度和鲁棒性。
In this paper we present a new Eulerian finite element method for the discretization of scalar partial differential equations on evolving surfaces. In this method we use the restriction of standard space-time finite element spaces on a fixed bulk mesh to the space-time surface. The structure of the method is such that it naturally fits to a level set representation of the evolving surface. The higher order version of the method is based on a space-time variant of a mesh deformation that has been developed in the literature for stationary surfaces. The discretization method that we present is of (optimal) higher order accuracy for smoothly varying surfaces with sufficiently smooth solutions. Without any modifications the method can be used for the discretization of problems with topological singularities. A numerical study demonstrates both the higher order accuracy for smooth cases and the robustness with respect to toplogical singularities.
