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In this talk,we first discuss some new variational models for the incompressible magnetohydrodynamics problem.Especially,a regularized MHD model with three unknowns is proposed,which may be used for an equilibrium model with plasma flows.Then we consider a mixed finite element method for the numerical discretization of the stationary incompressible MHD model in three dimensions with its velocity field is discretized using $H^1$ Lagrange nodal elements and the magnetic field is approximated by curl-conforming edge elements.Under the assumption that the original model has a unique solution pair,we derive a posteriori error estimates of the incompressible magnetohydrodynamic(MHD)equations with a sharp upper bound.Using these a posteriori error estimates,we construct an adaptive algorithm for computing the solution of 3D magnetohydrodynamics.Numerical experiments are carried out to show the performance of the adaptive finite element method.