Abstract
The aim of this paper is to extend the global error estimation and control addressed in Lang and Verwer [SIAM J. Sci. Comput. 29, 2007] for initial value problems to finite difference solutions of parabolic partial differential equations. The classical ODE approach based on the first variational equation is combined with an estimation of the PDE spatial truncation error to estimate the overall error in the computed solution. Control in a discrete Lnorm is achieved through tolerance proportionality and mesh refinement. A numerical example illustrates the reliability of the estimation and control strategies.
| Original language | English |
|---|---|
| Title of host publication | Adaptive Modeling and Simulation 2013 |
| Editors | J. P. Moitinho de Almeida, P. Díez, C. Tiago, N. Parés |
| Place of Publication | Barcelona, Spain |
| Publisher | International Center for Numerical Methods in Engineering |
| Publication date | 2013 |
| Pages | 187-198 |
| Publication status | Published - 2013 |
Keywords
- Defects and local errors
- Global error control
- Global error estimation
- Method of lines
- Numerical integration of pdes
- Tolerance proportionality