An adaptive time-filtered fully decoupled scheme for incompressible MHD equations

In this work, we propose a fully discrete, decoupled, and energy-stable finite element scheme for incompressible magnetohydrodynamics (MHD) equations. Using the constant scalar auxiliary variable approach with a stabilization parameter, all nonlinear terms and auxiliary variables are treated explicitly, which reduce computational cost. By incorporating the time filter technique, we construct a second-order time-stepping scheme with minimal modifications to the backward Euler discretization, and rigorously establish its unconditional energy stability. We also extend this scheme with adaptive time-stepping, where a low-cost error estimator dynamically adjusts the time stepsize to efficiently capture multi-scale features of the solution. Numerical experiments further verify the effectiveness and efficiency of the scheme for simulating complex MHD flows.