Numerical Identification of Initial Temperatures in Heat Equation with Dynamic Boundary Conditions

Chorfi, S. E.; Guermai, G. El; Maniar, Lahcen; W., Zouhair,

doi:10.1007/s00009-023-02461-8

Cited by 2 publications

(1 citation statement)

References 26 publications

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“…In ref. [43], the authors studied the inverse problem of numerically determining the initial temperatures in a heat equation with dynamical boundary conditions under additional data after a final time. The inverse problem was reduced to a Tikhonov minimization problem.…”

Section: Introductionmentioning

confidence: 99%

Numerical Reconstruction of the Source in Dynamical Boundary Condition of Laplace’s Equation

Koleva,

Vulkov

2024

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In this work, we consider Cauchy-type problems for Laplace’s equation with a dynamical boundary condition on a part of the domain boundary. We construct a discrete-in-time, meshless method for solving two inverse problems for recovering the space–time-dependent source and boundary functions in dynamical and Dirichlet boundary conditions. The approach is based on Green’s second identity and the forward-in-time discretization of the non-stationary problem. We derive a global connection that relates the source of the dynamical boundary condition and Dirichlet and Neumann boundary conditions in an integral equation. First, we perform time semi-discretization for the dynamical boundary condition into the integral equation. Then, on each time layer, we use Trefftz-type test functions to find the unknown source and Dirichlet boundary functions. The accuracy of the developed method for determining dynamical and Dirichlet boundary conditions for given over-determined data is first-order in time. We illustrate its efficiency for a high level of noise, namely, when the deviation of the input data is above 10% on some part of the over-specified boundary data. The proposed method achieves optimal accuracy for the identified boundary functions for a moderate number of iterations.

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Section: Introductionmentioning

confidence: 99%