Error Estimates and Superconvergence of a High-Accuracy Difference Scheme for a Parabolic Inverse Problem with Unknown Boundary Conditions
Year: 2019
Author: Haiyuan Yu, Liping Zhou, Shi Shu, Haiyuan Yu
Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 4 : pp. 1119–1140
Abstract
In this work, we firstly construct an implicit Euler difference scheme for a one-dimensional parabolic inverse problem with an unknown time-dependent function in the boundary conditions. Then we initially prove that this scheme can reach the asymptotic optimal error estimate in the maximum norm. Next, we present some approximation formulas for the solution derivative and the unknown boundary function and prove that they have superconvergence properties. In the end, numerical experiment demonstrates the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2018-0019
Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 4 : pp. 1119–1140
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Parabolic inverse problem unknown boundary condition finite difference method discrete Fourier transform asymptotic optimal order superconvergence.
Author Details
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Error estimate and superconvergence of a high-accuracy difference scheme for 2D heat equation with nonlocal boundary conditions
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https://doi.org/10.3934/math.20241352 [Citations: 0]