We study the approximation properties of piecewise constant functions with respect to triangular and rectangular finite elements in a metric defined on functions of bounded variation. We apply our results to a thin film model for martensitic crystals and to the approximation of deformations with microstructure.
|Original language||English (US)|
|Number of pages||21|
|Journal||Mathematical Models and Methods in Applied Sciences|
|State||Published - Mar 2003|
Bibliographical noteFunding Information:
This work was supported in part by AFOSR F49620-98-1-0433, by NSF DMS-0074043, and by the Minnesota Supercomputer Institute.
- Bounded variation
- Finite element
- Piecewise constant
- Thin film