Geodesic
The Reproducing Kernel Viewpoints of General Ritz--Galerkin Approximation
Matematičeskie zametki, Tome 112 (2022) no. 2, pp. 279-290

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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. 
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     author = {Zhiyong Liu and Qiuyan Xu},
     title = {The {Reproducing} {Kernel} {Viewpoints} of {General} {Ritz--Galerkin} {Approximation}},
     journal = {Matemati\v{c}eskie zametki},
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     volume = {112},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_112_2_a10/}
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Zhiyong Liu; Qiuyan Xu. The Reproducing Kernel Viewpoints of General Ritz--Galerkin Approximation. Matematičeskie zametki, Tome 112 (2022) no. 2, pp. 279-290. http://geodesic.mathdoc.fr/item/MZM_2022_112_2_a10/