Decoupled modified characteristic finite element method with different subdomain time steps for nonstationary dual–porosity–Navier–Stokes model

Abstract In this paper, we propose and analyze a decoupled modified characteristic finite element method with different subdomain time steps for the mixed stabilized formulation of nonstationary dual-porosity-Navier-Stokes model. Based on partitioned time-stepping methods, the mixed system with a stabilization term is decoupled, which means that the Navier-Stokes equations and two different Darcy equations are solved independently at each time step of subdomains. In particular, we solve the Navier-Stokes equations by the modified characteristic finite element method, which overcomes the computational inefficiency caused by the nonlinear term. In order to increase the efficiency, different time steps are used to different subdomains. We prove the error convergence of solutions by mathematical induction, whose proof implies the uniform L ∞ -boundedness of the fully discrete velocity solution in conduit flow. Finally, some numerical tests are presented to show efficiency of the proposed method.