Second-order modified characteristics FEMs for the time-dependent thermally coupled incompressible MHD equations

In this paper, we derive a second order characteristics finite element method for the time- dependent thermally coupled incompressible MHD equations. By using the temporal-spatial error splitting method, we present optimal error estimates for the second order characteristics finite element method unconditionally. The analysis is based on an iterated characteristic time- discrete system, with which the error function is split into a temporal error and a spatial error. Some numerical experimental results are given, which are consistent with the theoretical analysis in this paper.