Multivariate numerical derivative by solving an inverse heat source problem

2017 ◽  
Vol 26 (8) ◽  
pp. 1178-1197 ◽  
Author(s):  
Shufang Qiu ◽  
Zewen Wang ◽  
Anlai Xie
Keyword(s):  
Heat Source ◽  
Inverse Heat Source ◽  
Numerical Derivative

OPTIMAL ERROR BOUND AND A GENERALIZED TIKHONOV REGULARIZATION METHOD FOR IDENTIFYING AN UNKNOWN SOURCE IN THE POISSON EQUATION

2013 ◽  
Vol 12 (01) ◽  
pp. 1450004
Author(s):  
AI-LIN QIAN ◽  
JIAN-FENG MAO
Keyword(s):  
Heat Source ◽  
Numerical Experiment ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Stability Estimate ◽  
Tikhonov Regularization Method ◽  
Optimal Error ◽  
The Poisson Equation ◽  
Optimal Error Bound ◽  
Inverse Heat Source

In this note we prove a stability estimate for an inverse heat source problem. Based on the obtained stability estimate, we present a generalized Tikhonov regularization method and obtain the error estimate. Numerical experiment shows that the generalized Tikhonov regularization works well.

scholarly journals Inverse Heat Source Problem and Experimental Design for Determining Iron Loss Distribution

2021 ◽  
Vol 43 (2) ◽  
pp. B243-B270
Author(s):  
Antti Hannukainen ◽  
Nuutti Hyvönen ◽  
Lauri Perkkiö
Keyword(s):  
Experimental Design ◽  
Heat Source ◽  
Iron Loss ◽  
Loss Distribution ◽  
Inverse Heat Source

scholarly journals Inverse heat source problem for a coupled hyperbolic-parabolic system

2016 ◽  
Vol Volume 23 - 2016 - Special... ◽  
Author(s):  
Mourad Bellassoued ◽  
Bochra Riahi
Keyword(s):  
Heat Source ◽  
Parabolic System ◽  
Parabolic Type ◽  
Coupled System ◽  
Consolidation Model ◽  
International Audience ◽  
Inverse Estimation ◽  
Problème Inverse ◽  
Inverse Heat Source ◽  
Hölder Stability

International audience Dans ce papier, on a prouvé une estimation de stabilité de type Höldérienne pour un problème inverse de détermination du terme source de l'équation de la chaleur à l'aide d'une inégalité de Carleman pour un système d'équations hyperbolique-parabolique couplé. ABSTRACT. In this paper we consider a coupled system of mixed hyperbolic-parabolic type which describes the Biot consolidation model in poro-elasticity. Using a local Carleman estimate for a coupled hyperbolic-parabolic system, we prove the uniqueness and a Hölder stability in determining the heat source by a single measurement of solution over ω × (0, T), where T > 0 is a sufficiently large time and a suitable subbdomain ω ⊂ Ω such that ∂ω ⊃ ∂Ω. MOTS-CLÉS : Problème inverse, estimation de Carleman, système couplet

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