Abstract
This paper focuses on the modified characteristics finite element methods for the time-dependent thermally coupled incompressible MHD equations. We introduce characteristic time-discrete system by approximating the hyperbolic part with the modified characteristics tracting scheme. The error of the Galerkin FEM for the characteristic time-discrete system is τ independent. The unconditional stability and optimal convergence orders will be given. In order to show the efficient of the method, some numerical results will be given. The numerical results are consistent with our theoretical analysis, and our method is effective. The numerical method has a good robustness for different cases.
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