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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2022, Volume 25, Number 4, Pages 385–401
DOI: https://doi.org/10.15372/SJNM20220404 (Mi sjvm818) 		 
Solving the pure Neumann problem by a mixed finite element method

M. I. Ivanov, I. A. Kremer, Yu. M. Laevsky

Institute of Computational Mathematics and Mathematical Geophysics of Siberian Branch of Russian Academy of Sciences, Novosibirsk
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DOI: https://doi.org/10.15372/SJNM20220404
Abstract: This paper proposes a new method for the numerical solution of a pure Neumann problem for the diffusion equation in a mixed formulation. The method is based on the inclusion of a condition of unique solvability of the problem in one of the equations of the system with a subsequent decrease in its order by using a Lagrange multiplier. The unique solvability of the problem obtained and its equivalence to the original mixed formulation in a subspace are proved. The problem is approximated on the basis of a mixed finite element method. The unique solvability of the resulting saddle system of linear algebraic equations is investigated. Theoretical results are illustrated by computational experiments.
Key words: Neumann problem, generalized formulation, Lagrange multipliers, mixed finite element method, saddle point algebraic linear system, matrix kernel.
Received: 12.05.2022
Revised: 07.07.2022
Accepted: 18.07.2022
Document Type: Article
UDC: 519.632.4
Language: Russian
Citation: M. I. Ivanov, I. A. Kremer, Yu. M. Laevsky, “Solving the pure Neumann problem by a mixed finite element method”, Sib. Zh. Vychisl. Mat., 25:4 (2022), 385–401
Citation in format AMSBIB
\Bibitem{IvaKreLae22}
\by M.~I.~Ivanov, I.~A.~Kremer, Yu.~M.~Laevsky
\paper Solving the pure Neumann problem by a mixed finite element method
\jour Sib. Zh. Vychisl. Mat.
\yr 2022
\vol 25
\issue 4
\pages 385--401
\mathnet{http://mi.mathnet.ru/sjvm818}
\crossref{https://doi.org/10.15372/SJNM20220404}
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