High Accuracy Method for Magnetohydrodynamics System in Elsässer Variables

Abstract A method has been developed recently by the third author, that allows for decoupling of the evolutionary full magnetohydrodynamics (MHD) system in the Elsässer variables. The method entails the implicit discretization of the subproblem terms and the explicit discretization of coupling terms, and was proven to be unconditionally stable. In this paper we build on that result by introducing a high-order accurate deferred correction method, which also decouples the MHD system. We perform the full numerical analysis of the method, proving the unconditional stability and second order accuracy of the two-step method. We also use a test problem to verify numerically the claimed convergence rate.

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