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Space-time finite element method for determination of a source in parabolic equations from boundary observations

  • Phan Xuan Thanh ORCID logo EMAIL logo
Published/Copyright: August 6, 2020

Abstract

A novel inverse source problem concerning the determination of a term in the right-hand side of parabolic equations from boundary observation is investigated. The observation is given by an imprecise Dirichlet data on some part of the boundary. The unknown heat source is sought as a function depending on both space and time variables with an a priori information. The problem is reformulated as an optimal control problem with a Tikhonov regularization term. The gradient of the functional is derived via an adjoint problem. The space-time discretization approach is employed which allows the use of general space-time finite elements. The convergence of the approach is proved. Some numerical examples are presented for showing the efficiency of the approach.

Award Identifier / Grant number: 101.01-2017.319

Funding statement: This research was supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.01-2017.319. The final version of this paper has been done during the author’s stay at Vietnam Institute for Advance Study in Mathematics.

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Received: 2019-12-15
Revised: 2020-06-20
Accepted: 2020-06-24
Published Online: 2020-08-06
Published in Print: 2021-10-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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