标题： 利用观测器重构初始数据：半离散和全离散逼近的误差分析 显示英文标题

标题： Reconstructing initial data using observers : error analysis of the semi-discrete and fully discrete approximations

摘要： 一种新的迭代算法，用于从部分观测数据中求解初始数据反问题，最近在Ramdani、Tucsnak和Weiss [15] 中被提出。 该算法基于观测器（也称为Luenberger观测器）的概念，涵盖了大量抽象演化PDE的类别。 在本文中，我们关注该算法的收敛性分析。 更准确地说，我们提供了针对使用有限元在空间上和有限差分在时间上得到的半离散（在空间上）和全离散近似的完整数值分析。 该分析适用于具有有界观测（局部分布）的抽象薛定谔和波动保守系统。 显示英文摘要

摘要： 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).