Error Estimates for the Time Discretization of a Semilinear Integrodifferential Parabolic Problem with Unknown Memory Kernel. Issue 1 (20th February 2017)

• Record Type: Journal Article
• Authors: Grimmonprez, Marijke; Van Bockstal, Karel; Slodička, Marián
• Is Part Of: Numerical mathematics. Volume 10:Issue 1(2017)
• Page Start: 116
• Page End: 144
• Publication Date: 2017-02-20
• Subjects: 47J35, -- 65M12, -- 65M32; Parabolic inverse problem, -- convolution kernel, -- error estimates; Numerical analysis -- Periodicals; Numerical analysis; Periodicals; 518.05
• DOI: 10.4208/nmtma.2017.m1513
• Languages: English
• ISSNs: 1004-8979

Abstract

Abstract: This paper is devoted to the study of an inverse problem containing a semilinear integrodifferential parabolic equation with an unknown memory kernel. This equation is accompanied by a Robin boundary condition. The missing kernel can be recovered from an additional global measurement in integral form. In this contribution, an error analysis is performed for a time-discrete numerical scheme based on Backward Euler's Method. The theoretical results are supported by some numerical experiments.