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Zbl 0786.65108
Kunisch, K.; Murphy, K.A.; Peichl, G.
Estimation of the conductivity in the one-phase Stefan problem: Numerical results. (English)
[J] RAIRO, Modélisation Math. Anal. Numér. 27, No.5, 613-650 (1993). ISSN 0764-583X

For the one-dimensional diffusion equation, an iterative algorithm is proposed to estimate the transient conductivity coefficient from data obtained through a free boundary problem, the so-called one-phase Stefan problem, namely: $u\sb t = a(t)u\sb{xx}$, $0 < t \leq T$, $0 < s < s(t)$; $a(t)u\sb x(0,t) = g(t)$, $0 < t \leq T$; $u(s(t),t) = 0$, $0 \leq t\leq T$; $u(x,0) = \phi(x)$, $0 \leq x \leq b$; $\dot s(t) = -a(t)u\sb x(s(t),t)$, $0 < t\leq T$, $s(0) =b$. The conductivity coefficient is obtained by minimizing a cost functional (two of them are proposed) related to an approximated Stefan problem. Stability results for this problem guarantee the algorithm convergence, some numerical results obtained from actual implementations give support to the theoretical results.\par The paper is grosso modo self-contained.
[C.A.De Moura (Botafogo)]

MSC 2000:: *65Z05 Applications to physics
65M12 Stability and convergence of numerical methods (IVP of PDE)
35R35 Free boundary problems for PDE
35K05 Heat equation
80A22 Stefan problems, etc.
35R30 Inverse problems for PDE

Keywords: parameter estimation; numerical algorithm; stability; diffusion equation; iterative algorithm; transient conductivity coefficient; free boundary problem; one-phase Stefan problem; convergence; numerical results

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