About theoretical and practical impact of mesh adaptation on approximation of functions and PDE solutions
✍ Scribed by Alain Dervieux; David Leservoisier; Paul-Louis George; Yves Coudière
- Book ID
- 102209827
- Publisher
- John Wiley and Sons
- Year
- 2003
- Tongue
- English
- Weight
- 89 KB
- Volume
- 43
- Category
- Article
- ISSN
- 0271-2091
- DOI
- 10.1002/fld.503
No coin nor oath required. For personal study only.
✦ Synopsis
We try to formalize and study how mesh adaptation improves the approximation of interpolated functions or of PDE solutions. We ÿrst deÿne an adaptive solution, in the sense that the pair (mesh,function) satisÿes a non-linear coupled equation. In order to build optimal mesh adaptation strategies, we also deÿne a functional model, the 'continuous metric', which leads to propose the best mesh for a given function and a given norm. We then describe how convergence of adaptive solutions can be better than for non-adaptive ones; this involves some recent reÿnements concerning what we called early capturing of details, a speciÿc property of good adaptive strategies. We give some typical numerical illustrations. Convergence properties depend very much on how mesh adaptation is performed and we exhibit theoretical limits for the maximum order of accuracy reachable for some family of mesh adaptation methods.