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Matematicheskie Zametki, 2022, Volume 112, Issue 2, Pages 279–290
DOI: https://doi.org/10.4213/mzm13269 (Mi mzm13269) 		 
The Reproducing Kernel Viewpoints of General Ritz–Galerkin Approximation

Zhiyong Liu, Qiuyan Xu

School of Mathematics and Statistics, Ningxia University
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DOI: https://doi.org/10.4213/mzm13269
Abstract: In this paper, we introduce the new concepts of strictly positive definite functional and reproducing kernel functional space. We establish a connection between the strictly positive definite functional and the Ritz–Galerkin approximation. We prove a posteriori error estimate of the finite element method based on the reproducing kernel viewpoints.
Keywords: reproducing kernel, native spaces, Ritz–Galerkin approximation, functional, finite element.
Funding agency Grant number
National Natural Science Foundation of China 12061057
Natural Science Foundation of Ningxia Province 2019AAC02001
2021AA03006
NCET - New Century Excellent Talents in University (China) TJGC2018037
TJGC2019012
The research of the first author was partially supported by the Natural Science Foundations of China (no. 12061057), the Natural Science Foundations of Ningxia Province (no. 2019AAC02001), and the third Batch of Ningxia Youth Talents Supporting Program (no. TJGC2018037). Research of the second author was partially supported by the Natural Science Foundations of Ningxia Province (no. 2021AA03006) and the Fourth Batch of Ningxia Youth Talents Supporting Program (no. TJGC2019012).
Received: 27.07.2021
Revised: 03.02.2022
English version:
Mathematical Notes, 2022, Volume 112, Issue 2, Pages 294–302
DOI: https://doi.org/10.1134/S000143462207032X
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: Zhiyong Liu, Qiuyan Xu, “The Reproducing Kernel Viewpoints of General Ritz–Galerkin Approximation”, Mat. Zametki, 112:2 (2022), 279–290; Math. Notes, 112:2 (2022), 294–302
Citation in format AMSBIB
\Bibitem{ZhiQiu22}
\by Zhiyong Liu, Qiuyan Xu
\paper The Reproducing Kernel Viewpoints of General Ritz--Galerkin Approximation
\jour Mat. Zametki
\yr 2022
\vol 112
\issue 2
\pages 279--290
\mathnet{http://mi.mathnet.ru/mzm13269}
\crossref{https://doi.org/10.4213/mzm13269}
\transl
\jour Math. Notes
\yr 2022
\vol 112
\issue 2
\pages 294--302
\crossref{https://doi.org/10.1134/S000143462207032X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85136635359}
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