We derive a priori and a posteriori estimates for the error of the bi-linear interpolation polynomial for finite difference approximations of the solutions of parabolic systems on grids with irregular nodes. The estimates are developed for the $L\sp2$ norm, the $H\sp1$ semi-norm, and the $H\sp1$ norm of the error. We use the a posteriori error estimates of the interpolation polynomial to determine the 'high error' regions which require a finer mesh for computation. We derive and implement consistent computational stencils for the spatial derivatives at the nodes on the interface of regions of different levels of refinement. We use local error estimation and global computation / acase@tulane.edu
| Identifer | oai:union.ndltd.org:TULANE/oai:http://digitallibrary.tulane.edu/:tulane_25673 |
| Date | January 1998 |
| Contributors | Packard, Earl Dean (Author), Moore, Peter (Thesis advisor) |
| Publisher | Tulane University |
| Source Sets | Tulane University |
| Language | English |
| Detected Language | English |
| Rights | Access requires a license to the Dissertations and Theses (ProQuest) database., Copyright is in accordance with U.S. Copyright law |
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