Convergence analysis of a Crank-Nicolson Galerkin method for an inverse\n source problem for parabolic equations with boundary observations

2019/06/10 by Ðinh Nho Hào, Hao, Dinh Nho, Tran Nhan Tam Quyen +3
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Image and Signal Denoising Methods #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Optimization and Control (math.OC) #Ultrasonics and Acoustic Wave Propagation

paper · pdf · doi:10.48550/arxiv.1906.04732

openalex publication_date 2019/06/10 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

This work is devoted to an inverse problem of identifying a source term\ndepending on both spatial and time variables in a parabolic equation from\nsingle Cauchy data on a part of the boundary. A Crank-Nicolson Galerkin method\nis applied to the least squares functional with an quadratic stabilizing\npenalty term. The convergence of finite dimensional regularized approximations\nto the sought source as measurement noise levels and mesh sizes approach to\nzero with an appropriate regularization parameter is proved. Moreover, under a\nsuitable source condition, an error bound and corresponding convergence rates\nare proved. Finally, several numerical experiments are presented to illustrate\nthe theoretical findings.\n

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