Abstract
Some superapproximation and ultra-approximation properties in function, gradient and two-order derivative approximations are shown for the interpolation operator of projection type on two-dimensional domain. Then, we consider the Ritz projection and Ritz-Volterra projection on finite element spaces, and by means of the superapproximation elementary estimates and Green function methods, derive the superconvergence and ultraconvergence error estimates for both projections, which are also the finite element approximation solutions of the elliptic problems and the Sobolev equations, respectively.
| Original language | English |
|---|---|
| Pages (from-to) | 277-288 |
| Number of pages | 12 |
| Journal | Journal of Computational Mathematics |
| Volume | 20 |
| Issue number | 3 |
| Publication status | Published - 1 May 2002 |
| Externally published | Yes |
Keywords
- Finite element
- Interpolation operator of projection type
- Superconvergence
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics
- Computational Mathematics