2023/06/09 by Somia Boumimez, Boumimez, Somia, Carlos Castro +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2306.05712
openalex publication_date 2023/06/09 · openalex created_date 2023/06/13 · openalex updated_date 2026/07/28
A well-known boundary observability inequality for the elasticity system establishes that the energy of the system can be estimated from the solution on a sufficiently large part of the boundary for a sufficiently large time. This inequality is relevant in different contexts as the exact boundary controllability, boundary stabilization, or some inverse source problems. Here we show that a corresponding boundary observability inequality for the spectral collocation approximation of the linear elasticity system in a d-dimensional cube also holds, uniformly with respect to the discretization parameter. This property is essential to prove that natural numerical approaches to the previous problems based on replacing the elasticity system by collocation discretization will give successful approximations of the continuous counterparts.