A Galerkin Finite Element Method for the Reconstruction of a Time-Dependent Convection Coefficient and Source in a 1D Model of Magnetohydrodynamics

Autor:	Miglena N. Koleva, Lubin G. Vulkov
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	non-local parabolic operator magnetohydrodynamics flow system inverse problem Galerkin procedure finite element method iterative method Technology Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
Zdroj:	Applied Sciences, Vol 14, Iss 13, p 5949 (2024)
Druh dokumentu:	article
ISSN:	14135949 2076-3417
DOI:	10.3390/app14135949
Popis:	The mathematical analysis of viscous magnetohydrodynamics (MHD) models is of great interest in recent years. In this paper, a finite element Galerkin method is employed for the estimation of an unknown time-dependent convection coefficient and source in a 1D magnetohydrodynamics flow system. In this inverse problem, two integral observations are posed and used to transform the inverse problem to a non-classical direct problem with a non-local parabolic operator. Then, the non-classical strongly coupled parabolic system is studied in various settings. The equivalence of the inverse problem (IP) and the direct one are proven. The Galerkin procedure is analyzed to proove the existence and uniqueness of the solution. The finite element method (FEM) has been developed for the solution of the variational problem. Test examples are discussed.
Databáze:	Directory of Open Access Journals
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