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Error Estimates for the Time Discretization of a Semilinear Integrodifferential Parabolic Problem with Unknown Memory Kernel
Part of
- Equations and inequalities involving nonlinear operators
- Partial differential equations, initial value and time-dependent initial-boundary value problems
Marijke Grimmonprez, Karel Van Bockstal, Marián Slodička
Journal:

Numerical Mathematics: Theory, Methods and Applications / Volume 10 / Issue 1 / February 2017

Published online by Cambridge University Press:

20 February 2017, pp. 116-144

Print publication:

February 2017
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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.

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Error Estimates for the Time Discretization of a Semilinear Integrodifferential Parabolic Problem with Unknown Memory Kernel