On convergence of numerical solutions for the compressible MHD system with weakly divergence-free magnetic field

0574184 - MÚ 2024 RIV US eng J - Článek v odborném periodiku
Li, Y. - She, Bangwei
On convergence of numerical solutions for the compressible MHD system with weakly divergence-free magnetic field.
IMA Journal of Numerical Analysis. Roč. 43, č. 4 (2023), s. 2169-2197. ISSN 0272-4979. E-ISSN 1464-3642
Grant CEP: GA ČR(CZ) GA21-02411S
Institucionální podpora: RVO:67985840
Klíčová slova: compressible MHD * weak-strong uniqueness * stability * convergence
Obor OECD: Pure mathematics
Impakt faktor: 2.1, rok: 2022
Způsob publikování: Omezený přístup
https://doi.org/10.1093/imanum/drac035

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.
Trvalý link: https://hdl.handle.net/11104/0344532