论文标题
用于属于属的轴对称平均曲率流的有限差分方案的误差分析
Error analysis for a finite difference scheme for axisymmetric mean curvature flow of genus-0 surfaces
论文作者
论文摘要
我们考虑了零属的轴对称表面平均曲率流的有限差近似。对生成曲线的参数化的一个维偏微分方程的旋转轴的退化性的仔细处理使我们能够证明与离散的$ l^2 $ - 和$ h^1 $ -NORMS相对于完全离散的近似值。理论结果在数值收敛实验的帮助下得到了证实。我们还为某些Genus-0表面提供了数值模拟，包括用于平均曲率流的非安装自缩合器。
We consider a finite difference approximation of mean curvature flow for axisymmetric surfaces of genus zero. A careful treatment of the degeneracy at the axis of rotation for the one dimensional partial differential equation for a parameterization of the generating curve allows us to prove error bounds with respect to discrete $L^2$- and $H^1$-norms for a fully discrete approximation. The theoretical results are confirmed with the help of numerical convergence experiments. We also present numerical simulations for some genus-0 surfaces, including for a non-embedded self-shrinker for mean curvature flow.
