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Convergence of a crystalline approximation for an area-preserving motion
| Content Provider | Semantic Scholar |
|---|---|
| Author | Ushijima, TaKeo K. Yazaki, Shigetoshi |
| Copyright Year | 2004 |
| Abstract | We consider an approximation of area-preserving motion in the plane by a generalized crystalline motion. The area-preserving motion is described by a parabolic partial differential equation with a nonlocal term, while the crystalline motion is governed by a system of ordinary differential equations. We show the convergence between these two motions. The convergence theorem is proved in two steps: first, an a priori estimate is established for a solution to the generalized crystalline motion; second, a discrete W1,p norms of the error is estimated for all 1 ≤ p < ∞ and, passing p to infinity, a discrete W1,∞ error estimate is obtained. We also construct an implicit scheme which enjoys several nice properties such as the area-preserving and curve-shortening, and compare our scheme with a simple scheme. |
| Starting Page | 427 |
| Ending Page | 452 |
| Page Count | 26 |
| File Format | PDF HTM / HTML |
| DOI | 10.1016/j.cam.2003.08.041 |
| Alternate Webpage(s) | http://www.cc.miyazaki-u.ac.jp/yazaki/activities/pdffiles/2004UshijimaYazaki-JCAM.pdf |
| Alternate Webpage(s) | https://doi.org/10.1016/j.cam.2003.08.041 |
| Volume Number | 166 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
