On convergence of numerical solutions for the compressible MHD system with weakly divergence-free magnetic field
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00574184" target="_blank" >RIV/67985840:_____/23:00574184 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1093/imanum/drac035" target="_blank" >https://doi.org/10.1093/imanum/drac035</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1093/imanum/drac035" target="_blank" >10.1093/imanum/drac035</a>
Alternative languages
Result language
angličtina
Original language name
On convergence of numerical solutions for the compressible MHD system with weakly divergence-free magnetic field
Original language description
We study a general convergence theory for the analysis of numerical solutions to a magnetohydrodynamic system describing the time evolution of compressible, viscous, electrically conducting fluids in space dimension d (=2,3). First, we introduce the concept of dissipative weak (DW) solutions and prove the weak-strong uniqueness property for DW solutions, meaning a DW solution coincides with a classical solution emanating from the same initial data on the lifespan of the latter. Next, we introduce the concept of consistent approximations and prove the convergence of consistent approximations towards the DW solution, as well as the classical solution. Interpreting the consistent approximation as the energy stability and consistency of numerical solutions, we have built a nonlinear variant of the celebrated Lax equivalence theorem. Finally, as an application of this theory, we show the convergence analysis of two numerical methods.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA21-02411S" target="_blank" >GA21-02411S: Solving ill posed problems in the dynamics of compressible fluids</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
IMA Journal of Numerical Analysis
ISSN
0272-4979
e-ISSN
1464-3642
Volume of the periodical
43
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
29
Pages from-to
2169-2197
UT code for WoS article
000835418400001
EID of the result in the Scopus database
2-s2.0-85138478401