Abstract
We present a general error analysis frqmework for the finite volume element (FVE) approximation to the Ritz-Volterra projection, the Sobolev equations and parabolic integro-differential equations. The main idea in our paper is to consider the FVE methods as perturbations of standard finite element methods which enables us to derive the optimal L2 and H1 norm error estimates, and the L∞ and W∞1 norm error estimates by means of the time dependent Green functions. Our discussions also include elliptic and parabolic problems as the special cases.
| Original language | English |
|---|---|
| Pages (from-to) | 491-504 |
| Number of pages | 14 |
| Journal | Journal of Computational Mathematics |
| Volume | 20 |
| Issue number | 5 |
| Publication status | Published - 1 Sept 2002 |
| Externally published | Yes |
Keywords
- Error analysis
- Finite volume element
- Integro-differential equations
- Ritz-Volterra projection
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics
- Computational Mathematics