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

DOI10.1007/s00211-011-0408-xzbMath1235.65082arXiv1008.4737OpenAlexW2036375500MaRDI QIDQ663271

Karim Ramdani, Ghislain Haine

Publication date: 14 February 2012

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1008.4737

Mathematics Subject Classification ID

Wave equation (35L05) Schrödinger operator, Schrödinger equation (35J10) Numerical solution of inverse problems involving ordinary differential equations (65L09) PDEs in connection with control and optimization (35Q93) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

Related Items (12)

Iterative observer-based state and parameter estimation for linear systems ⋮ Output error minimizing back and forth nudging method for initial state recovery ⋮ Detectability and state estimation for linear age-structured population diffusion models ⋮ Numerical observers with vanishing viscosity for the 1d wave equation ⋮ Analysis of an observer strategy for initial state reconstruction of wave-like systems in unbounded domains ⋮ IMPROVING CONVERGENCE IN NUMERICAL ANALYSIS USING OBSERVERS — THE WAVE-LIKE EQUATION CASE ⋮ State reconstruction of the wave equation with general viscosity and non-collocated observation and control ⋮ Space time stabilized finite element methods for a unique continuation problem subject to the wave equation ⋮ A finite element data assimilation method for the wave equation ⋮ Approximation of the controls for the wave equation with a potential ⋮ Luenberger Observers for Infinite-Dimensional Systems, Back and Forth Nudging, and Application to a Crystallization Process ⋮ Data assimilation of time under-sampled measurements using observers, the wave-like equation example

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