Abstract
In this paper we consider finite element methods for general parabolic integro-differential equations with integrable kernels. A new approach is taken, which allows us to derive optimal Lp, 2 ≤ p ≤ ∞, error estimates and superconvergence. The main advantage of our method is that the semi-discrete finite element approximations for linear equations, with both smooth and integrable kernels, can be treated in the same way without the introduction of the Ritz-Volterra projection; therefore, one can make full use of the results of finite element approximations for elliptic problems.
Original language | English |
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Pages (from-to) | 51-83 |
Number of pages | 33 |
Journal | Journal of Integral Equations and Applications |
Volume | 10 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Dec 1998 |
Externally published | Yes |
Keywords
- Error estimates
- Finite element
- Integrable kernel
- Integro-differential
- Maximum norm
- Parabolic
- Superconvergence
ASJC Scopus subject areas
- Numerical Analysis
- Applied Mathematics