Abstract
An analysis is given for a class of nonconforming Lagrange-type finite elements which have been successfully utilized to approximate the solution of a variational problem modeling the deformation of martensitic crystals with microstructure. These elements were first proposed and analyzed in 1992 by Rannacher and Turek for the Stokes equation. Our analysis highlights the features of these elements which make them effective for the computation of microstructure. New results for superconvergence and numerical quadrature are also given.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1111-1135 |
| Number of pages | 25 |
| Journal | Mathematics of Computation |
| Volume | 65 |
| Issue number | 215 |
| DOIs | |
| State | Published - Jul 1996 |
Keywords
- Error estimate
- Nonconforming finite element
- Numerical quadrature
- Superconvergence