Algorithms for Computing Motion by Mean Curvature
Algorithms for Computing Motion by Mean Curvature
复制标题
通过平均曲率计算运动的算法
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
N. Walkington
中科院分区：
文献类型：
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作者：
N. Walkington
提出了一种计算平均曲率运动曲面运动的有限元算法。该算法使用水平集公式，因此可以适应曲面拓扑的变化。通过证明离散解同时满足$L^和$W^{1，1}$界，证明了系统的稳定性。建立了离散解的存在性以及与Brakke流的联系。文中还给出了一些数值算例及其在相场方程等相关问题上的应用。
We propose a finite element algorithm for computing the motion of a surface moving by mean curvature. The algorithm uses the level set formulation so that changes in topology of the surface can be accommodated. Stability is deduced by showing that the discrete solutions satisfy both $L^\infty$ and $W^{1,1}$ bounds. Existence of discrete solutions and connections with Brakke flows are established. Some numerical examples and application to related problems, such as the phase field equations, are also presented.