Error analysis in the reconstruction of a convolution kernel in a semilinear parabolic problem with integral overdetermination

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:275

Article

De Staelen, R. H.¹  Van Bockstal, K.¹  Slodicka, M.¹ 

[1] Univ Ghent, Dept Math Anal, Res Grp Numer Anal & Math Modeling NaM2, B-9000 Ghent, Belgium

关键词: Parabolic IBVP;    Integral overdetermination;    Convolution kernel;    Reconstruction;    Error analysis;   

DOI  :  10.1016/j.cam.2014.06.026

来源: Elsevier

【 摘 要 】

A semilinear parabolic problem of second order with an unknown solely time-dependent convolution kernel is considered. An additional given global measurement (a space integral of the solution) ensures the existence of a unique weak solution. The unknown kernel function can be approximated by a time-discrete numerical scheme based on Backward Euler's method (Rothe's method). In this contribution, an error analysis for the time discretization is performed of the existing numerical algorithm. Numerical experiments support the theoretically obtained results. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free