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

Author:

Thanh Phan Xuan1ORCID

Affiliation:

1. School of Applied Mathematics and Informatics , Hanoi University of Science and Technology , 1 Dai Co Viet Road , Hanoi , Vietnam

Abstract

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.

Funder

National Foundation for Science and Technology Development

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Estimation of soils thermophysical characteristics in a nonlinear inverse heat transfer problem;International Journal of Heat and Mass Transfer;2024-01

2. Identification of the forcing term in hyperbolic equations;International Journal of Computer Mathematics;2020-12-10

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