The Finite Element Method on the Sierpinski Gasket
The Finite Element Method on the Sierpinski Gasket
复制标题
Sierpinski垫片的有限元法
DOI：
10.1007/s00365-001-0010-z
复制
发表时间：
2001
影响因子：
2.7
通讯作者：
R. Strichartz
中科院分区：
文献类型：
--
作者：
Michael Gibbons;A. Raj;R. Strichartz
摘要。对于Sierpinski垫片上的一类分形微分方程，我们描述了如何用基于分段调和样条或分段双调和样条的有限元方法逼近解。我们给出了理论误差估计，并将其与使用该方法的计算机实现获得的实验数据进行了比较（可在网站http://mathlab.cit.cornell.edu/\sim gibbons上获得）。我们还解释了从实验数据中得到的关于拉普拉斯谱的一些有趣的结构。
Abstract. For certain classes of fractal differential equations on the Sierpinski gasket, built using the Kigami Laplacian, we describe how to approximate solutions using the finite element method based on piecewise harmonic or piecewise biharmonic splines. We give theoretical error estimates, and compare these with experimental data obtained using a computer implementation of the method (available at the web site http://mathlab.cit.cornell.edu/\sim gibbons). We also explain some interesting structure concerning the spectrum of the Laplacian that became apparent from the experimental data.