Recovering a coefficient in a parabolic equation using an iterative approach

Aliya S. Azhibekova

2016

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DOI 10.1063/1.4952317
Data confidence 70 medium
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Abstract

In this paper we are concerned with the problem of determining a coefficient in a parabolic equation using an iterative approach. We investigate an inverse coefficient problem in the difference form. To recover the coefficient, we minimize a residual functional between the observed and calculated values. This is done in a constructive way by fitting a finite-difference approximation to the inverse problem. We obtain some theoretical estimates for a direct and adjoint problem. Using these estimates we prove monotonicity of the objective functional and the convergence of iteration sequences.