Guaranteed estimates of functionals defined on solutions of stationary heat conduction equations and on their gradients
1 Department of Mathematical Modeling, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine
Keywords:
functionalities, stationary heat conduction equations
Abstract
We investigate the problem of guaranteed estimation the values of linear continuous functionals of stationary solutions of the thermal conductivity equation and gradients of solutions for their simultaneous noisy observation for quadratic deviation with unknown deterministic data. Guaranteed estimations for linear continuous functionals of the right hand sides of these equations are obtained.
References
[1] Y.K. Podlypenko, M.Y. Gorbatenko. Estimation of generalized solutions of linear elliptic equations, which allow mixed variational formulation // Bulletin of Taras Shevchenko National University of Kyiv. Series: Physical and mathematical sciences.- 2008.- Issue 3.- P.158-164.
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[3] Raviart P.A., Thomas J.M. A mixed finite element method for second order elliptic problems, Mathematical Aspects of the Finite Element Method, Lecture Notes in Math. 606, Springer-Verlag, New York (1977).
Cite
- ACS Style
- Gorbatenko, M.Y. Guaranteed estimates of functionals defined on solutions of stationary heat conduction equations and on their gradients. Bukovinian Mathematical Journal. 2016, 2
- AMA Style
- Gorbatenko MY. Guaranteed estimates of functionals defined on solutions of stationary heat conduction equations and on their gradients. Bukovinian Mathematical Journal. 2016; 2(2-3).
- Chicago/Turabian Style
- Mykola Yuriyovych Gorbatenko. 2016. "Guaranteed estimates of functionals defined on solutions of stationary heat conduction equations and on their gradients". Bukovinian Mathematical Journal. 2 no. 2-3.
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