Error estimates for structure-preserving discretization of the incompressible MHD system
Provides rigorous error analysis for structure-preserving methods in nonlinear MHD, benefiting computational fluid dynamics and plasma physics.
This paper proves optimal convergence rates for a structure-preserving discretization of the incompressible MHD system under CFL conditions, supported by numerical tests.
In this paper, we carry out the error analysis for the structure-preserving discretization of the incompressible MHD system. This system, as a coupled system of Navier-Stokes equations and Maxwell's equations, is nonlinear. We use its energy estimate and the underlying physical structure to facilitate the error analysis. Under certain CFL conditions, we prove the optimal order of convergence. To support the theoretical results, we also present numerical tests.