Reconstructing initial data using observers : error analysis of the semi-discrete and fully discrete approximations
Numerical Analysis
2010-08-30 v1 Analysis of PDEs
Optimization and Control
Abstract
A new iterative algorithm for solving initial data inverse problems from partial observations has been recently proposed in Ramdani, Tucsnak and Weiss [15]. Based on the concept of observers (also called Luenberger observers), this algorithm covers a large class of abstract evolution PDE's. In this paper, we are concerned with the convergence analysis of this algorithm. More precisely, we provide a complete numerical analysis for semi-discrete (in space) and fully discrete approximations derived using finite elements in space and finite differences in time. The analysis is carried out for abstract Schr\"odinger and wave conservative systems with bounded observation (locally distributed).
Cite
@article{arxiv.1008.4737,
title = {Reconstructing initial data using observers : error analysis of the semi-discrete and fully discrete approximations},
author = {Ghislain Haine and Karim Ramdani},
journal= {arXiv preprint arXiv:1008.4737},
year = {2010}
}
Comments
38 pages, 1 figures