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The Finite Element Method on the Sierpinski Gasket
| Content Provider | Semantic Scholar |
|---|---|
| Author | Gibbons, Michael Raj, A. Clement Louis Strichartz, Robert S. |
| Copyright Year | 2001 |
| Abstract | 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. |
| Starting Page | 561 |
| Ending Page | 588 |
| Page Count | 28 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s00365-001-0010-z |
| Volume Number | 17 |
| Alternate Webpage(s) | http://www.math.nyu.edu/~arjunraj/Publications_files/fulltext-1.pdf |
| Alternate Webpage(s) | http://janroman.dhis.org/finance/Related%20to%20Fractals/fractals/0010.pdf |
| Alternate Webpage(s) | http://rajlab.seas.upenn.edu/pdfs/gibbons_raj_strichartz.pdf |
| Alternate Webpage(s) | https://doi.org/10.1007/s00365-001-0010-z |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
