基于Stokes迭代的多层混合有限元方法求解稳态Boussinesq问题

he multi-level mixed finite element methods for the steady Boussinesq equations are discussed in this paper. The nonlinear coupled problem on a coarse mesh with the mesh size $h_0$ is firstly solved, and then, a series decoupled and linearized subproblems with the Stokes iteration are solved on the refined grid with mesh sizes $h_j(j=1,2,...J)$. Furthermore, the uniform stability and convergence results of the multi-level finite element method are derived with the mesh size $h_j$ under some uniqueness conditions. Theoretical findings show that the multilevel methods have the same order of approximation in $H^1$-norm as the one level method with the mesh sizes $h_j=h^2_{j-1}(j=1,2,...J)$. Finally, some numerical results are provided to investigate the effectiveness of the developed multi-level mixed finite element methods.