定常不可压缩磁流体方程组丰富多尺度稳定化有限体积算法研究

In the paper, the finite volume method for the steady incompressible magnetohydrodynamics(MHD) problem based on the lowest order mixed finite element pair on triangular mesh is considered, the linear polynomial is used to approximate the velocity and magnetic fields and the piecewise constant is adopted to approximate the pressure. In order to overcome the restriction of discrete inf-sup (LBB) condition, the multiscale enrichment method is employed. Firstly, the existence, uniqueness and stability of numerical solutions are established through the fixed point theorem. Then, the optimal error estimates of numerical solutions in H1 and L2-norms are presented. Finally, some numerical results are provided to verify the established theoretical findings and show the performances of considered numerical scheme.