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On convergence of numerical solutions for the compressible MHD system with exactly divergence-free magnetic field
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SYSNO ASEP 0562018 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On convergence of numerical solutions for the compressible MHD system with exactly divergence-free magnetic field Author(s) Li, Y. (CN)
She, Bangwei (MU-W) SAI, RID, ORCIDSource Title SIAM Journal on Numerical Analysis. - : SIAM Society for Industrial and Applied Mathematics - ISSN 0036-1429
Roč. 60, č. 4 (2022), s. 2182-2202Number of pages 21 s. Language eng - English Country US - United States Keywords compressible MHD ; consistent approximation ; convergence ; dissipative weak solution Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GA21-02411S GA ČR - Czech Science Foundation (CSF) Method of publishing Limited access Institutional support MU-W - RVO:67985840 UT WOS 000862256800008 EID SCOPUS 85138475265 DOI 10.1137/21M1431011 Annotation We study a general convergence theory for the numerical solutions of compressible viscous and electrically conducting fluids with a focus on numerical schemes that preserve the divergence-free property of magnetic field exactly. Our strategy utilizes the recent concepts of dissipative weak solutions and consistent approximations. First, we show the dissipative weak-strong uniqueness principle, meaning a dissipative weak solution coincides with a classical solution as long as they emanate from the same initial data. Next, we show the convergence of consistent approximation toward the dissipative weak solution and thus the classical solution. Upon interpreting the consistent approximation as the stability and consistency of suitable numerical solutions we have established a generalized Lax equivalence theory: convergence - stability and consistency. Further, to illustrate the application of this theory, we propose two mixed finite volume-finite element methods with exact divergence-free magnetic field. Finally, by showing that solutions of these two schemes are consistent approximations, we conclude their convergence toward the dissipative weak solution and the classical solution. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2023 Electronic address https://doi.org/10.1137/21M1431011
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